So I am on to act 4 and have spoken with the twins and I know how to get to the Tyrell building, but each time I go up there is a cop there who arrests me and I end up in jail. Have I missed something? Do I need to do something so that he doesn't appear? I have tried going off to do other things but when I come back he always seems to be there.

I walked right past him. Didn't run.

Not the security guard at the desk, as soon as I enter the screen there is a cop who says "your'e going down McCoy" and I end up in jail. There isn't even time for me to do anything. I have been on the screen previously when it was just the security guard, but now I have a cop right next to the grate that arrests me on sight.

In Act 4 you can't sneak more than once into Tyrell's meeting room. After the first time, they increase security and you'll get caught when entering the lobby from the grate.
If you didn't get the item from the meeting room, that is optional to complete the game, although it may affect slightly the outcome of the story.

Ah bother, that is probably it. I went into the lobby once but didn't go into the meeting room. I'm guessing the act of going into the lobby has triggered the cop appearing next time I tried to go back. I think I got stuck on this bit when it first released!