The Mindstorm stuff looks very cool; my older ds isn't yet old enough, so we've not been in there. I've never heard of a problem with spaces running out, but it's certainly possible; I think you could just go sign up first thing (go to the right as you enter and in a minute or two you'll come to it) and not have to worry at all. The Mindstorm system is basically simple robotics, I believe, with some computer-programmed instructions involved. You will probably have the chance to buy whatever they build; in the other building places at LL that's the case, but it is a pretty darned expensive way to purchase.
One hint I forgot to mention before: do your shopping mid-day; the Big Store especially gets very crowded near park closing. Then, when you pay for the item, ask to check the bag. They will put an ID sticker on it and take it to a place right near the exit (where the stroller rentals are) and you can pick it up at the end of the day. Also, they will give you the rest of the sheet of the same number ID, so anything else you get you have the clerk put it on and all your pkgs will be together when you get them.