Wasn't there some talk some months back about smart mining integration into the client?
Yes that is still planned, probably in the next full release after the one that is coming up now.
Is there any site or application that is tracking the current number of monero nodes (full nodes) that are on the network?
This site (link below) tries to track them but has issues with part-time nodes, and the site itself seems to be down right now. The best estimate seems to be 50-100 full time, several hundred part-time but up regularly. I'm sure there are more that are very part time, brought online only when people want to transact or check balances.
Hopefully that number will increase significantly in the future with smart mining (it is intended to minimize its resource footprint to encourage, or at least not discourage, people to leave it running in the background like a Bittorrent client) and some other things that are in the works.
http://cucjrcntebdskoljhpxj4xc3bmietslv7nfg5uy7itgrbgppcb6q.b32.i2p.us