The problem. By default, the field to be searched in the Quick Lookup area a the top of the nav bar, is the Contact field.
You can change it to any other field in the contacts area, but the next time you make a new search it will have reverted to Contact again.
Not a problem if it's the Contact field you always want to look in, but many users regularly need to search on something else, perhaps Company, or perhaps another field altogether, so each time have to change the field to be searched before doing the actual search.
In the installed software, one work around is to install the excellent free Default Lookup Field add-on from Exponenciel, but that doesn't help Act! users who work in the Act! for Web interface.
So, if it's such a big problem to have a simple control like default lookup field available to web users, could we not just make the field selection sticky? you choose the search field you want once and it becomes part of your personal preferences??