For me, advantages of assigned seats include:
1) Ability to choose your seat in advance
2) ~95% chance you won't have trouble keeping your seat if you board late provided some other passenger doesn't decide to snatch it from you before you get on (see my write up on seat poaching below).
3) In many cases, some of the better seats cost more, but you get more leg room. In business and first class, you typically get more legroom and more services.
Disadvantages of assigned seats:
1) Equipment swaps. Probably won't be an issue on Southwest as much as other airlines because they uses 737's. However, if your plane goes from a 752 to a 739, for example, now the seats are all jumbled up, and that wonderful bulkhead aisle you booked in advanced is now a middle seat several rows back. I won't even begin to get into the whole kerfuffle with groups (usually families with children) who have been separated due to an equipment swap.
2) Seat poaching. This is where someone is sitting in your seat (and this is one reason I personally try to board ASAP on AA when I fly it so I am far less likely to deal with this).
Sometimes it's a mistake, sometimes, they will sit there no matter what. If you have an unsympathetic flight attendant, you will be forced to sit where the poacher was supposed to sit, and it's usually the middle further back.
3) Drama surrounding "will you please trade me seats?" People will make up reasons or will try to guilt trip you in taking an inferior seat. Happens all the time.
Anyway, regarding seat poaching and seat trading, there are many threads outside of the Southwest RR subforum that are dedicated to these very issues. They span dozens of pages in many cases. Here is one of them:
Seat Swapping, Seat Poaching and Seating Etiquette: The Definitive Thread