You need to completely remove all the old silicone. All traces of it.
I used an olfa knife to scrape everything off, then alcohol to take any oil off, that might have been put on the glass by my hands.
Silicone does not stick to old silicone so if you only do the vertical corners, the new won't stick to the old silicone at the bottom seam. You might not need to have a water proof seal there, but why take a chance. Its just a little more work now, compared to maybe breaking the whole tank down later .
Make sure the silicone you use is approved for aquariums.
There is a lot of information on the web on DIY resealing an aquarium, this being the one I like.
http://www.youtube.com/watch?v=XKact...ayer_embedded#!