I occasionally browse AL.com to catch up on news out of Alabama, where I lived for several years. Out of curiosity, I went to GoDaddy.com to see who owned AL.net and .org, but when I typed in AL.net, I got the message "AL.NET is an invalid domain name. Minimum length error." Has there been some kind of restriction passed on two-letter domain names? It doesn't seem so, since AL.com is apparently online. I also tried AL.net on networksolutions.com and got the message "Please enter a valid domain name composed of three or more characters." What's the deal?

It looks like you just didn't dig deep enough. :-) Here's what I found at the first link below. Also check out the Wikipedia entry:

Two letter .com .net and .org domains were allowed with the Verisign registry. However, upon the transition of the management of .org to PIR (Public Interest Registry) the ICANN agreement placed all two letters domains in a reserved status. Under this agreement no two letters domains can be registered. All two letter domain names that are current and have not been deleted or expired will continue to operate.

All two-character labels shall be initially reserved. The reservation of a two-character label string shall be released to the extent that the Registry Operator reaches agreement with the government and country-code manager, or the ISO 3166 maintenance agency, whichever appropriate.The Registry Operator may also propose release of these reservations based on its implementation of measures to avoid confusion with the corresponding country codes.

both are working fine for me and there is no such restriction as you doubt.

The registrars for .net and .org may have set this restriction.

.com is from a different registrar.