Everyone will find their own problematic moments on vet mode.
I think my worst was on the Stalingrad mission where you need to blow up a tank that is circling a square, at the same time you're facing a good few waves of german soldiers coming at you. I spent a solid 4 DAYS on that level before I could scout out other checkpoints where I could attack that damn tank. Then I fell into a crater, lay low and as the tank drove right over me I planted the bomb and the tank blew up...
Another mission was Assault on Matmata or something (don't have cod2 anymore). The opening scene where your convoy is ambushed by a bomb and you're attacked from both sides by soldiers on rooftops. What a nightmare that opening scene was :/
Lastly, a map where you're holed up in some german HQ and you need to go out and take out a tank. The tank is just beyond a broken wall, so you need to climb over, shoot a few soldiers and run upto the tank to place the charge....
My advice:
1. As Phate said, keep pushing forward as you'll get a new checkpoint which pushes your whole offensive squad forward a bit.
2. Take your time, obviously you can't charge in. Vet mode is basically a one man war - ALL the enemy will be gunning for you and you only most of the time.
3. Learn to use smoke grens effectively. These things are a lifesaver and I found myself running out of them at the worst times.
4. Patience is key. The Silo map is where you need it as you'll be clearing 4 buildings of soldiers. The enemy is tightly nestled in on the top floor of most of these buildings, and each building is well designed for them to defend in. Sometimes you'll need to wait on the ground floor and plan your attack carefully as you approach each room above.
Vet mode was tedious enough to put me off the whole game, and I sold it once I got my points. It's not hard, it's just plain tedious. This game will wii you off like no other. See what I did there, I put wii instead of wee like!