There were 3 incidents in one day at Valencia that received a lot of publicity. Subsequent enquiries seemed to conclude they loaded in excess of what they should have needed, but weather conditions caused diversions and their contingency planning didn't cope.

https://en.wikipedia.org/wiki/Ryanair#Fuel_incidents

AV Herald article 1 2 and 3 about FR diversions in Spain in Summer 2012
Another piece about fog in BCN in Dec 2012 that caused non-FR diversions. The Irish Aviation Authority was saying that Spanish ATC has problems.

Thanks for the link, this is very interesting

Willie Walsh: Ryanair transformation is 'stunning'
 

Much better than they used to be
 

Flying weekly with Ryanair (on board a flight just now 🙄) they have improved immensely. I tend to book flights with them well in advance (sometimes upto 7 months in advance) and I do not think that you will get better value for money out there. As a result of their low prices, I sometimes will book two flights to give myself extra flexibility or will change at relatively short notice.

Of course they are not a legacy airline but I only use them for short hall flights. And yes, I have Priority Pass which helps from the lounge viewpoint!

The worst thing that I can say is that you cannot book a flight online a few hours beforehand which I have done with legacy airlines. All of the extra charges have only been applied due to my fault.

RYANAIR
 

I sometimes fly FR, but I have the following peeves

1) FR make a lot of money out of ground services, and everything in the airports they use (some almost exclusively!) costs more. For example, a beer in charleroi is about 5 euros. In an LH lounge, its free.
2) the airports are often in remote locations, so you are forced to drive (ok, you can take a slow bus). This means inevitably you will use the airport parking, which you need to add to the cost, and also fuel costs, speeding fines, wear and tear on the car etc. This can easily add 100 euros+ to your flight. It is harder to reimburse petrol and parking as business expenses than taxis. I bet FR gets a cut of airport parking.
3) Onboard, the seating is tight. You cant really move. its jolly uncomfortable
4) The airflow / oxygen flow is on very low setting, probably to save money. This means the air is bad on-board, and you can get sick easier.
5) FR planes fly full, so usually land fast and hard, as they are heavy
6) Hygiene - The toilets can be very dirty, and often the seats and carpet are dirty.
7) Onboard drinks and snacks, if you chose to consume also cost quite a lot extra. For a return flight, you can factor in 20+ euros additional cost. Saying this the food choice is actually bigger than on LH.
8) A newspaper (there is only 1 to chose from) costs 3 euros each way.
9) FR use different gates than other airlines. For example in Dublin, the FR gates are a long walk, compared to where LH flies from. At the FR gates, there is a lack of seats, which is, in my view deliberate to get people into the bars and cafes, where FR probably takes a cut, and prices are typically quite high. On LH, you can sit in a nice lounge.
10) FR terminals tend to be very crowded
11) Hand baggage. On LH, I can get away with a laptop bag and a wheely bag. On FR, 1 cabin bag is max allowed. Often this bag must be placed under the seat, as bins are often full.
12) Choosing a seat costs extra. On FR, if you dont pay, you often get the middle seat.
13) There is no in-flight magazine, just a catalogue of adverts
14) There is no seat pocket
15) The life jacket is lesser quality (in my view) than on LH
16) last minute flights are often more expensive than LH
17) On the newer FR planes, seats are very thin. The old one had less leg room, but in some ways where more comfortable
18) No recline on the seats
19) FR wont wait for a connecting flight
20) Print your own boarding pass. The process to print is not very easy. If you forget to do this, you must pay a lot at the airport -60 Euros ?
21) Less staff per passenger than LH

Plus points
1) Walk to the plane. I am not a big fan of the airport bus
2) some routes are very convenient with good timings
3) if you travel light and stick to all the rules, it can often be cheaper
4) Eastern European flight attendants are friendly
5) out of town airports are small and can be quick to transit

Plenty of incorrect data in there, and quite a few things I'd disagree with:
1 - is ridiculous. Most people won't have *G status, especially if they fly lufthansa on shorthaul, where earning *G (for lounge access) is difficult. Please provide an actual price comparison when purchasing beers outside the lounge.
2 - partially fair. With public transport it can be a different story, e.g. STN is cheaper to get to than LHR from certain parts of the UK/London. Many locations they still fly into the main airports, e.g. I've been to AAR, KRK, ZRH, BSL (no real alternates for those though).
3 - LH, LX, BA are all just as bad for comfort, especially on newer/refitted planes.
(4 - no idea, haven't compared air flow)
5 - Same as point 3, most legacy carriers in Europe are just as "heavy" and full. Nevermind that the legacy carriers have A321s which would tend to have harder landings since they're significantly heavier in comparison.
(6 - haven't compared, can't say BA are great though)
7 - fair, don't rely on onboard food.
8 - partly fair, I haven't had particularly good newspaper access on most of my flights on legacy carriers though, except with lounge access, see point 1 again.
9 - partly fair - they definitely go for the cheaper terminals. But lounge access is only for those with status, most people don't get that, so not really fair to compare lounge to terminal.
10 - same as 9, cheaper terminals.
11 - fair, but you can get overhead space if you bother lining up early.
12 - you can't exactly choose seats on SH in Europe until checkin, slight advantage in that you can change seats for free at that point, but no advance seat selection.
13 - fair, but these magazines are usually trash anyways
14 - fair, and annoying
15 - lol, really? Have you ever used these lifejackets? How do they differ?
16 - fair. But last minute you're screwed regardless of airline.
17 - meh. Point 3 again, all seats are equally bad in europe.
18 - I'd say this is a positive. Back to point 3, all euro flights are cramped, not reclining removes an additional pain point.
19 - duh. Do FR even sell connecting flights?
20 - slightly annoying, but it's really not that hard to print stuff. And it's 15 euros / gbp, not 60. Moreover they have an app nowadays.
21 - Maybe, but considering some staff are mainly for business, you probably have more staff per passenger on average in the main cabin.

Considering the price differentials I usually see, the food/newspaper fees are a minor factor. Transport costs vary hugely, and that's just a trip specific thing to take into account. Other than that the differences really aren't that significant.

Regarding the hand luggage, you're now allowed 2 pieces.
The main hand luggage and a smaller bag.

Also the mobile app check in and boarding passes are very convenient and quick to do.

One must wonder, how would they know if an OP have a non-EU/EEA passport unless they check passports at the gate, at which point they can check whatever they want, so why does an OP have to go to their landside desk for a "document check"?

Also, for flights within Schengen, what is there to even check? It is not like they can deny someone from boarding if he fails to present them with a valid Schengen visa.

Their website seems to say "Non EU/EEA passengers must do this in order to ensure compliance with immigration authorities", but then that would have been the requirement from all airlines, I can easily board any KLM flight from AMS to any other Schengen country without showing my passport (or providing API) even once.

Ryanair do check ID at the gate. One assumes this is a revenue generation exercise by Ryanair. It has nothing to do with government regulations in any case, particularly on internal Schengen flights.

How is it generating any revenue? Isn't it causing just the opposite by having to have agents available for this "document check" ?

non reclining seats on a short flight are big bonus for me , saves having some slob reclined in my face for the whole flight

You don't really need more gate agents just to check ID, it usually doesn't slow the line down (the bottleneck is either waiting for a bus, or boarding the actual plane).

I've never done any Schengen internal flights on Ryanair so I haven't really noticed this myself (all my flights were to/from UK, where they have to check IDs...). But my other flights generally haven't checked IDs except for possibly flights from Poland.

But this special ID check for non-EU/EEA passport holders is done before security.
My question is... why not just do it at the gate like every other airline does, if at all.

It saves time at the gate. Staff have to check that the passport is with or without a visa. They can't have an encyclopedic knowledge of every country's regulations, so can lookup this up easily at the desk. At the gate, doing this could waste time.

Other airlines may check less thoroughly at the gate only, but they'll face the cost (plus potential fines) of returning passengers who are turned away at their destination for having the incorrect documentation. Ryanair's model tries to prevent this by properly checking the documents.

Even within Schengen, you are still required to carry the correct travel documents.