On petfinder you cannot:
Search by key words in descriptions like "mellow" or "fluffy"
Exclude a breed or breeds from a search
Sort the results by oldest or newest listings
Exclude or include listings that specify things like "must own a house with yard"
Exclude or include listings where the dog is being transported hundreds of miles
There are two main issues--one, the data collected from the shelters is pretty spotty. Some shelters enter descriptions that are, well, descriptive. Other shelters copy and paste the same thing every time. Although petfinder attempts to offer a filter for "kids in home", shelters provide poor data so that you will still get tons of results for "cannot have kids". This is not entirely the developers' fault, though they could validate and enforce some aspects of the data coming in.
The other problem is just that there really is not much development gone into this site. Why not have the descriptions indexed for searching by key phrases? Why not put a posted date on each listing?
This site could be amazing and much more helpful to animals if it had more work put in. I don't know if it's a funding thing or what.