A white sediment is normal. As they ferment, the brine turns cloudy, and when it sits for awhile, it settles out as a sediment. I'm not sure what the sediment is, but it's caused by the fermentation process. Sauerkraut has the same thing, it's just not as noticeable.
If your pickles smell good, taste them. If they taste good, eat them.

If there's anything really wrong with a ferment, you'll know it! It will smell bad and taste bad (and usually there will be a visual clue as well).