In Prem 6 there's a little button with two arrows on it to the left of the timeline, this allows you to click on an individual clip and automatically select all the clips after it, so you can click on the first clip after the gap and drag all following clips back with it to close the gap.
and repeat for each gap.
There's probably a really basic name for this, but I only know that it has a little double-arrow symbol on it.
hope that helps and doesn't confuse further.
Panasonic SD9, Panasonic NVGS-75, Canon MV600i