Some feedback...

The recent searches look terrible when you enter many airports:


Then when you enter an airport code and hit comma, it doesn't resolve the airport until you've moved on to the next field:



To be honest, I find those grey "bubbles" quite annoying. They don't add anything to the user experience, especially when they only say "JFK" or "CPH" anyway - what's the benefit with displaying them with the grey background and airport symbol? That only takes up a lot of space. The old behavior was much better - it would also let you search for an airport, but you could also just enter a list of airport codes. You can still do that now, but you always get that error message until the input field loses the focus.
I mean, look at this:



Compared to this:



Then in general I agree that it's harder to navigate the form with the keyboard. I was super quick with the old layout. I appreciate that you're trying to make this more user friendly, but most users will probably be very experienced with both searching for flights and the interface. So what would help an inexperienced person actually slows down someone who uses the application every day.
I also find it extremely confusing that the routing codes and extension codes for outbound and return are now placed next to each other and smaller. I often have quite a lot of codes there and it just felt more natural the way they were placed. Because I read the form from the top to bottom - so with the old Matrix, for a flight LAX-MIA, I'd read the form as LAX, routing/extension codes, MIA, routing/extension codes. With then new form, I read LAX, MIA, routing/extension codes, routing/extension codes. Which I find confusing. But maybe I'll get used to that.

I think it would really help if you could add some sort of "grouping" to the form, like different background colors, or the drop shadow that you use on the results page (when click through to a specific flight). Especially with the multi-city search, there's only a thin lightgrey line separating the flights. It's super hard for my brain to figure out which fields belong to which flight. With the old Matrix, flights were visually separated in a much better way. At the minimum, it would be good if the padding around the horizontal lines could be increased.

Then the prices in the airline filter menu are overflowing, so it's really hard to read them. Since there are scrollbars anyway, you might as well add a bit more space:



The times aren't properly aligned, so it's difficult to compare durations. Either flight times should be padded (i.e. 06h50m) or they should be aligned better in some other way. I would personally also prefer "6:50h" over "6h50m" - it's just easier to read.



And then on the results page, the booking class is cut off at the buttom. E.g. for "Economy", it's looking more like "Economv":



Hope that this is helpful. :-)