Not much wrong with 64-bit Windows in general. I've been using Windows XP x64 since the early days. The application compatibility was very good. In general the only applications that didn't work, were applications that used some kind of low-level drivers, such as CD/DVD protection or firewall/virus scanning/defragmentation stuff. Another standard issue was software which still used a 16-bit installer.
I found that often I could run the software if I just installed it under a 32-bit OS, and then copied over the installed files to the 64-bit OS. For games, funny enough a no-CD/DVD patch would often fix the game to run 64-bit.
By the time Vista was released, most vendors had 64-bit drivers, so things went pretty smoothly from then on. And with Windows 7, 64-bit is ready for prime-time.
I would not recommend XP x64 however. Not because it's a bad OS, I've had good times with that OS, in the early 64-bit days, and still keep an installation around on one of my partitions. But it's basically 'orphaned': Microsoft does not support it. Not even things like Windows Live Messenger are supported on XP x64. The installer refuses to install it.
And although nearly all hardware comes wtih 64-bit drivers these days, XP is generally not among the supported OSes. Vista and Windows 7 can in most cases share the same drivers, as the driver model is nearly identical. And the 32-bit and 64-bit versions of these OSes use the same kernel version. XP 32-bit and XP 64-bit are not the same OS. XP 64-bit is NT 5.2, a cousin of the Windows Server branch. XP 32-bit is NT 5.1.