What is the limit on finding items in TF2? How can I tell if I have hit this?

Solution 1:

According to the official Team Fortress 2 Wiki page:

The current item drop system was introduced on April 20, 2010. Players are guaranteed to find items at regular intervals of 30 to 70 minutes, with an average interval of 50 minutes. [...] There is no cap on the amount of items that can be received per week, but instead a cap on the amount of playtime in which drops can occur. This cap has been estimated to 10 hours each week ([resetting] every Thursday). Playing beyond the cap won't yield additional items. Playing less than the cap carries over unused time to the next week, increasing that week's cap to a maximum of two weeks' worth of playtime. [...] Receiving a Mann Co. Supply Crate or any usable item does not count against the cap...

And to answer your question of "and if I hit this limit of gameplay, how do I tell?", I guess you could time yourself playing for 70 minutes, and if you don't receive any items, you've hit the cap.