Just another (hopefully) helpful post for anyone that is having trouble when performing a network update.
I was doing a few adjustments to my multipress installation and noted that I suddenly started to get an error when using the "update network" feature. The error was:
Warning! Problem updating https://support.indieunite.com. Your server may not be able to connect to sites running on it. Error message: SSL certificate problem: unable to get local issuer certificate.
After looking at the error logs (which reported nothing) and some other things, I found that the problem was being caused by curl (the command line tool for transferring data with URL syntax)...
To be honest, I have not used curl much (except by just installing it and letting the site do what it needs to do) so I can't give much advice about configuring it with SSL. In the end I didn't need curl anyway so removed it from the server and the errors stopped occurring.
There's info about curl and SSL at http://curl.haxx.se/docs/sslcerts.html if you really need to use it and having these problems.