Occasional system hangups after upgrade to Lion: is it a disk or software problem?

Nobody will tell you for sure (without diagnosing a problem), but you should definitely check both your harddrive and memory (corrupted memory may cause data loss while writing to HD. I had such a problem twice in my life.)

I prefere non-OS specific utilities:

SystemResqueCD

You can install it either on CD or on USB flash drive. It contains a lot of diagnostic utils. One of them is memtest86+ which you can use to test you memory.

Memtest86+

It's is one of the most recognized software diagnostic tools on the planet. Since 2008 it supports Apple hardware. It checks memory by writing different binary patterns and checking what's actually stored in memory.

memtest86+ screen

Red means bad

MHDD

Official site of this utility is dead, but you can find in here. That's what you need to check your hard disk drive. I'm not sure that it will work on Apple hardware, but you can plug your hard drive in any PC or in external USB enclosure and check there.

MHDD checks HDD


It was a software problem, specifically a botched Google Chrome complaining about 'not being signed in to Chrome'. I have never signed up to Chrome (I am the only user) and never attempted to do so.

While I am not sure of this, all the above problems disappeared once I removed and re-installed Chrome. None of the hardware or software tests I run showed problems to my hardware or system.