Why can't I install OS X 10.6.6 combined updates?

Sounds like some sort of silently corrupted download (I had an old router that did this occasionally). Try a different connection using completely different modems, routers and access points. Maybe even a different internet provider at a friend's house or office.

This really sounds like a corrupted download problem -- the "invalid checksum" and "The file couldn’t be opened because it isn’t in the correct format." errors strongly point to this. Check the image file's size and SHA1 hash (note: Apple includes the hash in their download pages, e.g. here). Here's what I get on the 10.6.6 combo update (in disk image format):

$ ls -l MacOSXUpdCombo10.6.6.dmg 
-rw-r--r--@ 1 gordon  staff  1054916500 Jan  6 04:10 MacOSXUpdCombo10.6.6.dmg
$ openssl sha1 MacOSXUpdCombo10.6.6.dmg
SHA1(MacOSXUpdCombo10.6.6.dmg)= 868768cbc88db1895161f74030e98e8ce2303151

If your downloaded files don't match this length and/or hash, start digging into what's going wrong with the download. Do all of you downloaded files have the same lengths and hashes as each other (i.e. how consistent is the damage)? Try downloading with different browsers, via different internet connections, etc (you might want to use a smaller test file, like the 10.6.1 update, if you find one that shows similar errors). Look for a pattern in the errors and try to isolate where the problem's coming from.

The issue is "The file couldn’t be opened because it isn’t in the correct format.".

I would try the following steps:

1. Download using the "Software Update" program, not manually. Perhaps "Software Update" will do something differently, or the manual version is including something that shouldn't be included

2. Find out the md5 hash of the DMG you are downloading. Verify this. If the md5 hash doesn't match, then there is a problem with the download. Try downloading with a different browser. Try downloading via a different ISP.

3. If the md5 hash matches and you get this error, that means one thing. If the md5 hash doesn't match, then this error is expected, and this means something else. You need to know which it is. Leave a comment and further debug steps can be considered at that point.