My interview questions

I've always been surprised by how few people ask any technical questions at an interview. There's plenty of posts that are much better than mine on this subject. My favorite is this one: http://steve-yegge.blogspot.com/2006/03/truth-about-interviewing.html

I'm often tasked with evaluating the basic technical competence of an individual. This is commonly known as the "bad cop" around here. I think that's undeserved, as the technical part of the interview is my favorite part. I'd much rather design another object-oriented elevator than discuss what my greatest weakness is, or how I dealt with a problematic co-worker.

Anyway, I wanted to share my interview questions. If you are going to get interviewed by me, it's likely that you'll end up some variants of these. The good candidates get through then in short order so we can get onto more important things. These were modeled after Steve's recommendations from above. These allow for more in depth probing after the initial answer is obtained.

1. Write a C function that counts the number of bits set in an unsigned int. What about signed?
2. Tell me about polymorphism, and why it is useful. How could this be done under the hood?
3. You have a singly linked list of addresses, sorted by the person's name. There's millions of entries. We need to provide the linked list to some other entity at some point so it at least needs to keep the sorted linked list format. What are some ways to speed up the lookup of an entry?
4. We have a directory (say on an SMB share so anybody can access it) that has an arbitrary number of sub-directories. These directories may or may not have sub-directories, but they do have an arbitrary number of text files. These text files contain IP addresses in the dot-decimal format like so:

10.127.13.3
10.127.14.5
10.127.13.16
10.127.13.241

I generated these files incorrectly, and any IP address that has a zero in one of it's fields is printed incorrectly:
10.127..1
10..1.3
10.127.14.
.1.2.3
127...1
...1

should be really printed as
10.127.0.1
10.0.1.3
10.127.14.0
0.1.2.3
127.0.0.1
0.0.0.1

How can I find these bad IP addresses and can I fix the easily?