NT4 had many serious BSODs. SP6 was so problematic due to a critical bug in LSA that it was re-released as SP6a.
Windows bugs have moved more and more into the 'edge case' territory. Not that major issues don't crop up for "everyone" today, but BSODs used to be much more common. Part of that was due to the architecture, thus drivers, but the other side of it was core Windows functionality that just had bugs.
Kernel is almost perfect these days. Can't say the same about user environment. Explorer and shell are buggiest ever.
Explorer is the shell ;)
But Explorer has had it's fair share of issues. I have a 98SE machine to prove the stalls, lockups, lack of refreshing directories, etc...
Not anymore, not entirely. Start menu and taskbar are now in a separate thing I believe. Welcome to 20s!
Explorer.exe is still the shell -- the shell is defined at HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Winlogon\Shell, if you want to look (or replace it).