The auto save feature is pretty neat, as it'll save after every completed mission, mission replay, random encounter, activity, in short: anything of relevance.
The auto save feature won't save after you improve a skill, however, and if you're in flight school or in the shooting range, you'll have to leave those before the auto save feature does its job.
However, the quicksave feature (accessible from the cellphone) is pretty neat too. Try it out, and you'll never want to go back to your safehouse to save, never. Well, maybe you'll occasionally want to return to change clothes, watch TV, fetch whatever vehicle is in your safehouse garage, or to time travel 6 ingame hours into the future.
The beauty about the quicksave feature, is that it'll save your current position, the vehicle you're currently driving (but not its damage, which is kinda nice) and is just perfect to abuse the stock market. Just quicksave in front of the assassination missions, start the mission, jolt down the stock you'll want to invest in, load the previous quicksave, then invest in those stocks as everyone (as you won't be able to switch while on assassination mission).
Basically, auto save does a good job, but quicksave does an awesome one. Use it well and do it often.
This could as already stated be a sign of a hardware issue in the PS3 itself, However don't overlook the possibility of it being a television problem. Try hooking up to another tv, and if that does not fix the problem there may even be something up with the AV or HDMI cable you are using. if swapping out these things does not help and you are still under a warranty I would recommend downloading all your save files to flash drives and return the ps3 for a new one.
as for the heat problem try to keep your PS3 in a well ventilated area. if this does not help it is more than likely either due to some sort of heat sensor problem or something to do with the fans.
Best Answer
Depends on weather you want to replay a mission/start over from that point or not OR if you care about neatness.
If you save only on Slot 1 you will overwrite the previous save, you will not lose a single second of game play, you simply lose the option to start the game from that past point, instead you will start the game from the new save point. For instance you might want to save before the Assassinations missions, as sometimes the Stock market goes weird (I lost my investment actually) and if you DON'T overwrite your save, and save at Slot2 ,you can go back, with all your money and stuff and start over as if you never played.
On the other hand I save only on Slot 1 as I don't care about replay-ability (as I've finished the game before) and I used to have a problem on my GTA-SA following which is the save I want to use when I go back to the game after months of not playing.
TLDR: You generally save on Slot 2+ if you want to be able to replay a mission later, or you are more than one person using the Device, otherwise it doesn't matter.