Yes unfortunately the terrible twos do arrive well before they actually turn 2.
My stepdaughter, turning 3 in oct started them around that age as well.
I would suggest not putting him in his cot as 'time out' as he will then start to associate his bed with being naughty which isnt what you want. Find a designated area, a corner or even a spare room in your house, away from distraction. It takes a bit of work to get them to stay but they do learn.
I would have to suggest the teaching of feelings. This worked exceptionally well with my step daughter as when she was 'sad' this made us 'sad'. And we all know kids want to please their parents!
I guess also the trick is (as hard as it appears) is not to get flustered or embaressed if your son behaves like this in a public place because they just FEED off of it! They know well and good that you have no power in a supermarket. But its making them believe that you do. But what you do is a good thing, if he misbehaves, then home you go, or at least back to the car. Showing him that he doesnt get to go out and have fun when he plays up will eventually sink in. (dont buy treats for him while you're out b/c then he will expect them, leading to more tanties.)
Praise him when he is good, but lack of attention when he performs is also essential. In their book, any attention is good attention. But its the good behaviour you want to focus on and get him to focus on.
Thats all i can think of atm. Just hold your ground and remember to pick your battles.