How to check the last solution publish report

You can check the last solution publish report, go to the solution screen and select the option.

Platform Server:

solution report
In fact, in recent versions of version 5.0, 5.1 and 6.0 you can even "attach" to an ongoing Solution Publication (launched by you or some other developer) and see its progress in realtime, which is a very cool feature.

Just click on the link inside the orange box on the Solution page (see sample below).