This is best explained by examples.
Go to the sandbox and try to do a search (using the Contact Search block) starting with the % wildcard (for example "%bob"). You can't. As soon as you type the "%" it is erased and the field filled with unrelated text. This makes first-name searches through the search box, for example, impossible.
Further, if you type a name at a reasonable rate of speed, you are likely to erase your text completely with each letter. The odd behavior here is that the suggested text causes the entire field to be highlighted, and this erased, instead of just the suggested stuff. For example, typing "Sam" often nets me "Salvi, Barbara A." or maybe "a member, a member" depending on how quickly I type. Not what I was looking for, either way.
Going over to the standard or advanced search page such searches work fine. The problem is with the nifty, AJAXy-interface stuff. I'm sorry I can't write a more technically succinct issue on this one.