I want to add a large number of search feeds and tweet buttons to my website - over 100. Do they all need a separate widget Id? Is there a limit to how many I can create?

Dear Jon,

No, there is no any limit on the number of search feed and tweet buttons . If you want to use the same search feed on all pages , you can just use the same widget id.

According to what I can read on twitter there is a limit of 100 widgets.

dev.twitter.com/discussions/18032

dev.twitter.com/discussions/22125

What I'd really like is one widget where the user can type in the hashtag that they want to see displayed in the widget.

Dear Jon,

It means that there is actually a limitation from Twitter.
Unfortunately a widget with the functionality you mentioned does not exist.