I caught fall flounder at the beach area during the winter season. And some fish are more common during certain seasons, but I -think- you can catch any fish regardless of season, just you'd have to go to different locations (or find schools of fish) to find them. I could be wrong on it though.
Don't tempt me to do better. I'm lazy and shall continue at a snail's pace.
squid (for calamari) is awesome for RP and I found out you really only ever catch it after 6 pm. I think you might catch more of them in the summer than in spring but that could be due to my improving rods and fishing skill.