It's not that the programming is sloppy, or shortsighted, it's that it was designed and a character needed to be set aside for certain functions...

If a company had a name like.. oh.. Wal*Mart then a computer would see the * and assume that you meant a group of letters you didn't know. $am's Club thinks that you want a single wild-card character and will bring up Tam's Club and Jam's Club. If 30 years from now someone starts using a name like... Bl*$ule the computer won't recognize it properly. Why? Because some 'short sighted' programmer didn't realize that someone would put a $ in their name?

By the way, you also can't use a hyphenated o, that e with the little letter on top, or any number of other things. Names with numbers in them are seen as 'wrong' and cause confusion.

Having worked in databases and programmed a few I've seen the limitations and workarounds. They aren't pretty. You either Dummyproof the entry (Letters only! No Spaces!) and something like an apostrophe gets lost, or you don't and the first secretary who puts in the record says "O Keefe" and the second one puts in "O'Keefe" and the third puts in "OKeefe" which are all different names.

Sigh...

Time for people to start referring to eachother as SSN numbers. "Hi I'm 430239910"

No confusion, no problem.

Johnny '); DROP TABLE, anyone?
(xkcd)

*writes down*

What's your credit card number?

Which is sloppy and shortsighted when the characters are used as input.

You analogy doesn't quite match. At the moment, there are no places calles Bl*$ule, while those characters have been used in databases since quite some time.

Apostrophes on the other hand have been used in names since long before there were computer systems.

The problem here is that in several database systems, text strings (such as names) are enclosed in apostrophes as well. These database systems don't have any problems dealing with apostrophes: when there is an apostrophe inside the string, you double it. That way the database knows that the string hasn't ended yet which means there are no problems.

The problems arise when a programmer doesn't think about the possibility of an apostrophe in someone's name. Everything a user enters into a computer system is checked before it's used (yes, even the comment I'm typing now). When a programmer forgets that an apostrophe is a valid character, (s)he can decide to block a user from entering apostrophes as part of their name. The reason for this is that this apostrophe can break the database (at least, if that same programmer forgets that they need to double the apostrophe before sending it to the db).

Basically, if you have a name with an apostrophe, and a computer system refuses your name because of that, there are probably more problems than just that. It's also quite likely that security is wonky.