E8500 OC paired with the ATI HD 5870 = bottleneck?

Completely depends on what you do. DDR2 and DDR3 ram aren't much different in many games and apps, although I always notice a difference between DDR2 at 667mhz and DDR2 at 800mhz.

Games that are geared to work with quad cores and the i7 (which is a quad core...) will cause you some bottle neck. Theres not many out right now though that are made to utilize quads. Duo is still the most common type of architecture used in games, so for right now in almost all games I wouldn't expect much bottle neck.

It's mainly the future you're looking at... Within the next 1-3 years theres going to be a lot more games and programs that are going to use quad cores. That's when you'll start to see bottle neck, but by then we'll probably have dx12 and whole new GPUs.  

But what I was wondering was if the E8500 or the DDR2 will slow or cripple to many extent the ATI HD 5870 or the 5850.

with quad 3.8GHz and HD 5870, u will survive for about 2-3 years, your system is great...  

Its just a duo core. I have never had slow downs with 2 cores and all the experts say games run better on 2 cores unless the game is coded to use the other cores. Still not many multithreaded games so ..I don't own a quad yet.

I think fgocards summed it up pretty good for you.
In newer games that are optimised for 4+ threads, you will lose out on some performance but it should still be perfectly playable.
With the rest of the games, you will be just fine.
You could drop in a quad core CPU, however I would recommend saving for a future platform upgrade at this point.

There is NO performance difference between DDR2, DDR3 or any 'high speed' variants of either.

ups, sorry, my mistake, it just core 2 duo not quad core...  
Agree with outlw6669, get HD 5870 now and safe your money for a new build system later...
Your current system is good...

I still have DDR1 memory and the 5870 is screaming fast.

^+1
yup, it doesn't show a significant different when using DDR1, DDR2 or DDR3 when gaming...

No real difference with gaming or much else really.
As the speed increases, so does the CAS Latency making the effective access time virtually identical.

A handy chart:

From Here

The e8500 is a very fast cpu still... you should hold on to it another year or so to get your money out of it. You probably wont see any slowdown until then anyhow.