How do I troubleshoot a lockup that occurs when plugging in an external monitor? Since installing Lion, nearly every time I plug my 13" MacBook Air into my 27" Dell display, the Mac locks up.  (The mouse pointer stops moving.)  I can't do anything except shut it down and reboot.

How do I troubleshoot this?

Update: It looks like my DELL U2711 is broken...

I got a kernel panic on my MBA, and since rebooting, each time I plug in the Mini DisplayPort cable the display shows a DisplayPort icon and then goes into power saving mode.  The same thing happens when I try Detect Displays on my MBA.

I tried a different DisplayPort cable (full-size DisplayPort plug on each end) with my DELL laptop running Windows 7, and saw the same problem.  And then same thing happens when I try Detect Displays.

So it appears the problem is with my cable or my MBA, but the display.

Nonetheless, it's still an Apple hardware and/or software bug if my MBA locks up when I connect a defective monitor.  But it's unlikely to be fixed since it's unlikely to be reproduced by an Apple engineer.

Update #2: I got a new DELL U2711 display (which works with my MBA using a the Mini DisplayPort cable).  My MBA is locking up again when I plug the cable in, unless I reboot first and plug in before logging in.

I submitted Problem ID 10259810 on https://bugreport.apple.com/.

Update #3: I just tried connecting the DEL U2711 without rebooting first, now that I'm running OS X 10.7.3: my MBA did not lock up. (They may have fixed it prior to 10.7.3—I haven't tried to reproduce this problem for quite a long time.)
Since the mouse pointer gets frozen, you can be pretty confident that the lockup is happening deep down in the system - kernel extensions, hardware interrupt type things.

Assuming you have a great backup and don't mind futzing a bit (and I'll also assume you haven't extra cables, monitors, macs to just eliminate one thing at a time) you can surely try booting again in Safe Mode. 

To boot in Safe Mode, hold the shift key down - it will bypass all non essential kernel extensions and may or may not help you isolate the issue.

It's best to be systematic when troubleshooting - so I'd try that one guess, then be more logical about it.

Why not start with the "bible" on Isolating issues in Mac OS X? 

Don't forget you get 90 days of support from Apple - you can hit them up on AppleCare (800-APL-CARE or online - express lane) - they have a standing exception for people that cover software purchases for support - even if your hardware is out of the free software support timeframe. 

The wisdom to isolate software before hardware is probably the best call here - even though it's a monitor and clearly buggy. What are the odds that Lion and the hardware failed at the same time? It's possible and you might be able to take your Air to another monitor with your adapter / cable and rule that out.

Good luck, and happy hunting - partner!