Yep - I can relate to that in an office systems environment, and remember that 10.7 (Lion) was a major release, almost an architectural change in many aspects.
There are so many variables involved it's enough to make everyone's head spin. I don't have a problem doing it on my home machines though - they are in an all-Apple environment from connection (TimeCapsule) to AirPort network to Macs to iOS devices to AppleTV and it's a closed system that is carefully maintained and kept stringently clean. Never a problem that I've found so far - and they're non-critical. I'n not overly cautious but by the same token not stupidly eager either.
At work, I wait for a week or two before upgrading - but we're on an all Apple environment there too and have had very few problems if any over time. I guess that the more connectivity you have to non-Apple devices, devices and drivers the more problems you're likely to encounter - seems natural. As far as your Parallels problem, I'd be looking at the vendors... NAS server issue - were the vendors privvy to the betas as part of the Mac developer program? I'll bet they were. Same for the VNC issue. It's hardly a surprise when any major OS is released - either Windows or otherwise. They're discussed for months ahead of any release date.
Were your IT personnel pre-checking and performing any real due diligence prior to your upgrades?
EDIT: LOL... having said all of that, VMware Fusion won't work any more - an upgrade needed from v4.1.1 to v4.1.3 seems to be required.