Will a sata3 SSD work properly on a Mac mini (Mid 2010) with 2.4 GHz CPU?
Yes, you can.  

Here are the theoretical bus speeds 

SATAI   - 150 MB/sec - 1.5 Gb/sec
SATAII  - 300 MB/sec -  3 Gb/sec 
SATAIII - 600 MB/sec -  6 Gb/sec

In theory, a very fast drive could saturate a SATA2 bus, but if it does, it will still send the data, just slower than it's capable of.  If that bothers you, just buy a slower SATA2 SSD drive.

Regardless, you'll be very happy with the performance upgrade over a slower drive.  It's the best upgrade investment you can make.