That particular feed issue is common on guns that have a worn carrier dog spring.
That's the spring that powers the shell lifter.
Try to get a Police gun version, it's a stronger spring that helps prevent feed issues.
Usually a good cleaning and replacing that spring cures the problem.
As for other springs, it's good to replace the magazine spring, preferably with a Police version spring, IF you have a 4 shot magazine.
The Police 4 shot mag spring is a heavy duty spring that insures reliable feeding when shooting the gun fast.
Just on general principles you might replace the extractor spring, although disassembling the extractor, spring, and plunger and cleaning them and the hole in the bolt is usually enough.
To get new springs, you can use Brownell's or Midway, both of whom sell NEW factory parts, not used or after market.
Here's a schematic of the 870 at Brownell's. You need the carrier dog plunger spring part number 10 to fix the feed issue:
http://www.brownells.com/schematics/Remington-/870-Standard-Weight-12-16-20-sid134.aspx
I think Brownell's sell Police model springs, you'll have to ask.
So, a new, preferably Police model carrier dog spring, a Police 4 shot magazine spring, and a standard extractor spring (there is no special Police extractor spring) should fix you up.
NOTE: If Brownell's can't supply Police springs, just order direct from Remington.