After hearing some people were able to get into the warrior guild tunnel by clicking from a specific spot, I was bound and determined to figure out the dwarven cave thing. I have not tried to reproduce this but let me know if it works for you!
I was at 1024x768, not sure if that matters. I tried standing in every location i could to click on the cave entrance, no luck. So just for fun, I picked up one of the shovels laying around and tried to drop it on the entrance - no luck BUT, when I dropped it and clicked on the cave entrance really quickly a bunch of times, VOILA! I was IN!
Let me know if it works for you.

I did have problems getting into the Dwarven Tunnels but I managed eventually by lots of clicking an and around the entrance.
I didn't have to use the Warriors Guild trick to get in.

Just outside the tunnel are 2 patches of rotten food on the ground, stand immediately south of the one on the right and gradually keep going further south until the tunnel mouth turns white when the mouse hovers over it..