I just beat Call of Duty 3 on veteran today and I have to say it was definitely one of the harder to beat in the series. I only did about 2 or 3 missions a day to avoid disliking the game to the point where I simply didn't want to even put it in my 360.
Advice for those in the process or looking to complete this game:
I think the most difficult part of this game is simply the amount of time and objectives that must be completed in between each check point. I often found myself repeating certain sections five or six times which I successfully completed the first time through just because the last objective before the checkpoint is triggered was very difficult and I died without knowing exactly what to do. I think I still managed to beat the game in about 5 or 6 days but all I can really reinforce is patience. If you have the patience to try over and over you will be able to beat the game on veteran. Some parts seem very lucky and some parts I simply would take cover and let the seemingly useless AI cover me for a certain amount of time triggering new objectives, other times I would simply rush the AI and try to complete objectives early instead of waiting to kill seemingly endless chains of enemies. It's all about experimenting with certain situations and seeing what works. If you die going to the left 5 times in a row try going to the right, or if you just can't seem to stay alive when you physically try to thin out herds of enemies simply take cover and leave your xbox for 15 minutes to take a break. Come back in 15 and see if the AI has thinned the enemies enough for you to progress. Lastly, as I just mentioned it a little in the previous statement don't forget to take breaks. If you are stuck on a certain checkpoint do not be afraid to turn off your xbox and pick it up later. It really helps to just take a break and try it again later.
That is my two cents on the game and if you have any questions about specific parts of the game feel free to message me over live and I can try and let you know how I progressed past certain parts of the game.