Expert is very easy if you can simply change the way you play. You cannot possibly enter an Expert game with the mentality of another difficulty.
Friendly fire - Don't even bother shooting if there's more than a 50% chance of hurting a fellow survivor in the process. It causes major annoying damage and can really hurt.
Zombies - The Common Infected do 20 damage on a front hit and 10 damage for a back hit. The best thing? They have to actually come right up to you to do said damage. Try headshotting with the shotgun, or using one of the rifles but always aim for the heads.
Play with full captions on. You will get many notifications as to incoming attacks and Special Infected spawns, but do note that you should listen for the music cues anyway. If you like to play with music off, at least turn it on a little bit. It really does help.
On Campaign mode, you can actually hear tanks BEFORE you trigger them. On Versus, they just spawn and boom, but no: on Campaign mode, you can hear a tank and it's only after walking past a door or something they are activated. This gives you time to prepare, and it's even possible to see part of a tank before it gets activated.
MOST IMPORTANT TANK RULE:
Setting a Tank on fire makes it FASTER on Campaign and activates a Fire Timer (something like 40 seconds on Expert mode?) before it dies. Any shooting you do when it's on fire is actually a waste of ammo (although sometimes, especially with a rifle or mounted gun, it slows it down a bit). Just try running to the saferoom if you've used your molotov or gas can. There's no need to shoot.
I believe this is the same for Witches, so do not bother shooting witches on fire either unless you like wasting ammo. I doubt it slows her down.
And Tanks and Witches can both enter the beginning saferoom, Tanks sometimes struggle and certain positions help prevent it but it is sometimes possible for both to enter (with a Tank, however, it's slightly more unlikely).
My final tip is to play with the controller sensitivity all the way up, both vertically and horizontally, in the pause or main menu. Takes a long long time to get used to, but you will find you can aim much faster and you have freedom of movement. And be aware! Always look behind you and in front of you - you almost need eyes in both directions at once.
If you're only aiming for this one, do a campaign you know the most thoroughly. Their difficulty is about the same.
There is actually a glitch to beat every finale without so much as killing a single Infected. On No Mercy you can let zombies break down a door and then go into a room where the AI can't see you, on Dead Air you can jump on top of the plane by moving one or two carts with propane tanks, on Blood Harvest you can actually just stand and melee a tree and everything will immediately die before it reaches you (!) and on Death Toll there's a rock you can sit on. Crash Course, as far as I know, has no finale glitches, however Crash Course on Expert doesn't count towards it anyway. But I'm not going into how they work and not saying you have to use them. It has little relevance, just find them out through Google or YouTube.
Don't forget you MUST SURVIVE the finale and ENTER THE RESCUE VEHICLE! It's for surviving a campaign, not only for completing one.
Hope this helps.