I have always been confused about the use of dielectric grease until reading this(sorry about the long cut and paste, but I believe it's worth it, also don't know the guys credentials, but it sounds like he knows what he is talking about.):

As written by Wayne Orwig, MGNOC Georgia State Rep.

Using Dielectric Grease on connectors.

A lot of people use dielectric grease on connectors. Some people mistakenly believe that dieletric grease is a conductor. In fact, it is just the opposite; it is an insulator. Dielectric grease is typically made of silicone grease.

As an insulator, dielectric grease is good for use on spark plug boots. This was one of the original applications on vehicles when the high-energy ignition systems came out. It can help insulate the connector and, in particular on a motorcycle where it can get wet, it waterproofs the spark plug boot. And, because it is silicone, it is fairly stable at high temperatures and won't affect the rubber and plastics.

So why would you put an insulator on a connector? The idea is that you use a thin layer. When you push the connector together the grease is pushed out of the way enough to get a connection and the surrounding grease then keeps out water and oxygen. The connector will be protected from the environment and less likely to corrode. Plus, the silicone is safe for the plastics and PVC insulation.

That sounds good, so far; so why not smear it on everything? Well there are a number of good reasons.

First, silicone grease outgases constantly. If the silicone gas gets near a connector or a contact, such as a relay, and there is a spark, the spark at the contact can create silicon dioxide. Some people even suggest that the silicone gas from dielectric grease can travel many feet through the unsulation on a wire and damage a contact on the other end. Omron states that even their sealed switches can be damaged by nearby silicone grease outgassing. Reference the following links for more info:

http://www.omron.com/ecb/products/pdf/en-d2vw.pdf

Lubricating electrical switches Archive content from Machine Design

Second, it is an insulator. It can prevent contacts from touching. If you do use it, use a very thin layer.

Third, if you have a corroded connection, silicone grease will not help. In fact, it may make it worse. It can never improve anything. Dielectric grease will never make a poor connection better.

Fourth, it attracts dust and dirt and it hardens over time. This means that if you smear a lot of silicone grease on connectors you may see nearby relays, switches, or points fail later on. Since silicone grease does nothing at all to improve the connection and, in fact, may insulate the contacts in the connector increasing the resistance the connector may still fail.

So what do you do? Look for a contact enhancer/lube. While most contact cleaners are simple solvents that just wash the connector off there are contact enhancers that deoxidize the contact surface and actually work to lower the contact resistance (make a better connection). Most contact enhancers leave a lubricant behind that protects the metal and continue to deoxidize the metal and improve the connection. They can work to lower the resistance and make a better contact as time goes by. The best you can hope for from dielectric grease is that it seals it enough to not get worse. I have used Caig Deoxit on my bikes for a few years now. I first found out about this on my job when I had to correct an issue in a connector system that could not tolerate even 5 thousandths of an ohm of resistance drift. We had a connector in the field that had been improperly plated and was starting to drift, mostly in warm humid areas like Florida. Our testing showed that the Caig Deoxit could be a good long-term fix. We ended up using the Deoxit to stabilize the bad units until we could get corrected wiring harnesses built with the correct connectors. We also put a layer of Deoxit on the new parts to protect and keep them clean over their lifetime. This solved the drift issue that we had.

I still use a small amount of silicone grease on my spark plug caps. It helps to waterproof them and makes it easier to pull the cap off, but I use it in very small amounts and never near a relay or switch.

 

If you want to use a Dielectric Grease, use one specially formulated for electrical connections:
GM (General Motors) - 12377900 - GM/AC Delco Dielectric Lubricant For Electrical Connections
They key is to use in moderation. Too much can actually hydrolock the connection and push terminals out. More is not better, just a light coating on the terminals.

Another solution is Stabilant-22A.
Stabilant 22 Contact Enhancer from R.A.L. Audio Services, pro audio dealers