The cards that it says I've unlocked aren't in my inventory. Do you just get them after the whole event? I have two from just buying games actually in my inventory, but the cards I've 'unlocked' aren't around. I'm Steam Level 7, so I know they should be dropping...
You need to be Steam Level 8 before you're awarded any of the cards you've unlocked. According to the Monster Summer Game FAQ:
How do I get Summer Sale trading cards?
Play the Monster Summer Game
If you’re Steam Level 8 and above, you’ll get a Summer Sale trading card at random intervals while playing, up to three per 24-hour period. (If you reach Steam Level 8 before the end of the sale, you’ll be granted the cards you earned by playing the Monster Summer Game).
An earlier version of the FAQ incorrectly stated that level 5 was required.