Playstation likes to be difficult with Skyrim. We played on one for a couple of years before finally going to PC. Skyrim on PS3 lags and crashes. There seems to be no way around that.
Something that seems to effect it is loose items. I've read even items stored in containers can effect lag, but haven't noticed that. If you have a house with a bunch of stuff laying on tables or even displayed on walls, it will be laggier. I learned this in both the Falkreath and Pale custom homes. Things were ok until I built my armory, and the more stuff I displayed, the laggier it got. Then I did some testing. I once took that round tower room at the back of the house, and just loaded it up with loose loot. Everything I looted got dumped, piece by piece, into that room, watching the game get laggier with every load of loot. I had a pile about thigh-high, when it switched from incredibly slow to mostly frozen. It would literally freeze in place for 60 seconds or more, then move me one step, repeat. Experiment over, reloaded the save I'd made right before starting and could run, jump, and fight again.
What helped us was keeping our save files down to the three most recent (not autosaves). Also, every so often, I would plug a usb drive into the PS3 and save my most recent save file to it.
If you do uninstall and reinstall, make sure you do that first. You can then copy it right back to the PS3 and play as though you'd never left.
What seemed to help us the most, with crashes/lag, was turning off all autosaves. They seem to take up an enormous amount of process, especially when you fast travel and then end up fighting. I think I ended up leaving save on rest/sleep active, because I knew I was going to sleep at home and I could control when I rested. I got into the habit of making a save every so often, or when I acquired a new item, reached some achievement, that I didn't want to lose. At the end of the game, I'd delete all but three.
The other big helper was the 30 day wait, which on the PS3 is a bit tedious. It should take you about 10 minutes, but go someplace safe/free to sleep. Sleep for 24 hrs, 30 times. (I usually did 31, just to be sure). That helps reset all the dungeons, gets rid of things left open, laying around, etc. These are all more things the game doesn't have to worry about rendering while you play. It even made a discernible difference in load screen times.
Of course, If you get the chance to play on a fast PC, you'll be blown away by the difference.