Not GPS related, but the day I am really worried about is January 19th 2038 3:14:07AM... Unix time will roll over if stored in a signed four byte integer field.
Or slightly later the use of a 2-digit year in x509 certificates. The standard assumes that dates with year <50 are 20xx, and >=50 are 19xx. It doesn't help that this is one of the best designed, most understandable, and well-thought-out parts of the x509 standard.
We’re already seeing problems from that. It will be handled, probably without the financial bonanza of 2k, but as such will probably cause more problems.