Plugins used to fix HDSL limitations in premier
 

Looking to create a list that people use.

Noise: use neatimage
For jittery footage: Use Mercalli 2 (convenient) or deshaker(free). Not an image stabilizer like mocha which doesn't deal with jello effect caused by the jitter. Use the fix borders for slightly bad footage and down-sample project to 720 for really bad footage. Can take a good handheld shot and make it look like a very expensive shot.
Color correcting bad white balance: Magic bullet collorista II
to fix dead pixels: CC Simple Wire Removal, just pick a spot and it gets rid of them.