Whenever Dogmeat dies I get a crash to the desktop with the error message "The instruction at 004d2b03 referenced memory at [always different number]. The memory could not be read from. Click on OK to terminate the application."
This is particularly annoying at the moment as I'm currently fighting Deathclaw in the cave at the Hub. Using a flamethrower got me through it no problems the first time, but after forgetting to save I can no longer do it without Dogmeat getting in the way of the flames and dying after only one or two shots, causing the game to crash. Testing it outside of the fight, it is definitely the death of Dogmeat that cause the game to crash and the death of any other party member doesn't have the same reaction. The crash has happened when using both a flamethrower on him and using an assault rifle.
Anyone know a solution?

I would think this is just a random bug, one of which is a victim of circumstance rather than something old. To quickly get round the problem I would use a Character and/or Inventory Editor from "No Mutants Allowed" to pump your character up, (say so you have 200 AP) so you can kill the thing in one round of combat.
I had a similar problem in the Morningstar Mines, one slap from one those those sukkas crashed the game. After I killed one, I re-saved the game, edited my character back to what it was and everything was fine.
My advice would be to simply get out of the situation ASAP, then re-save the game once you're at a safe location.
You can download save editors and the such like here.
If you really don't like this idea, try to just run away or distract the Deathclaw :/ but it sounds like you've tried this.
Good luck!

I'm not actually stuck in the fight. My save is at the entrance of the cave. So, I could just leave and find a different weapon to finish him off with, or just completely ignore him.
My main concern is that this means I will have to keep Dogmeat alive throughout the whole game. He is really strong and I haven't had any problems with him staying alive until this point, but I can imagine the chances of him surviving fights is only going to get slimmer as I progress further (particularly if I continue to use the flamethrower.)
Thanks for the help (and I'm trying it out now,) but is there anyone with a more permanent solution? Even a way of removing Dogmeat from the party would be good enough.

Well, if he survives to the last level, he will basically die no matter what because of some awkwardly places force fields that he apparently ignores and runs through on a consistant basis. Sooo... yea. Getting him to the end of the game is an achievement itself.

Well that is good to know :)
If that is the case, then finishing the game with this bug sounds like it will be pretty much impossible.

I would advise trying to load a earlier save and seeing if you can kill him from that save. Find out if the bug is gone or not.
Other things you could try if that doesn't work are getting him killed in from different sources perhaps one way it won't crash out.
Locking him into a room with only one entrance and shutting the door. He will teleport to you when you change screen but maybe that wil sort the bug out. Just some random ideas that may change something in the game and avoid whatever is causing the crash.

As great as the fallout games are they do tend to have these completely random nonsensical bugs that have completely random nonsensical solutions. Glad its working eitherway now though.

Looks like the problem has surfaced again. This time it keeps crashing when I'm in a fight with the mother deathclaw in the basement at the Boneyard. I think it is when I'm taking the killing shot on the mother, as two of the times it has happened I've looked at the mother deathclaw before attacking and I get the message saying "almost dead." But before the animation is played (which is slightly different from the previous time as I was seeing Dogmeat die before the crash,) I get a crash to desktop with the same error message as before.

I use the 1.3.5 community patch plus the 1.21 patch, and I had the game crash once killing the glowing mutants underneath Necropolis.
I strongly suggest people patch the game with the community patches.

It definitely seems to be the deathclaws that cause me problems.
I did as you suggested, Ralackk, and didn't encounter any problems. When I decided to return to that area and fight the deathclaws it crashed in my second or third battle with one of the regular ones.
I'll give gamebin's suggestion a try.