Starfox: Well, I'll give you the way I do it myself (work each time) but of course, spoilers involved so those who are not there... don't read.
First, in this part of the game, there is only one thing you really need to do: take the briefcase and a hint on opening it. Everything else (aside a little something) is secondary and you can come back later to check what you may have missed.
So:
Enter the lodge and immediately close the balcony door behind you. Take a look at the briefcase, Tex notices that it is handcuffed so you have to find the key. Turn around a pick up the wallet, take what's inside and put back the wallet on the table. Open the closet doors and pick up the clothes. Search them, you find a key but sadly not the right one. Put the clothes back in place and DON'T shut the doors. It will save you some time later. Go to the kitchen and open the top right drawer (the closest to the door you came in -- at this point it's a good idea to save the game -- Now examine the little something in the drawer, position yourself so you can conveniently reach the door without being forced to turn around then pick up the vial. At this point the phone should ring. Close the drawer (required) go through the door then into the closet, turn around and close the closet doors. You don't need to worry about the kitchen door, it closes itself.
It's safer if you don't move or pickup anything else in the lodge aside the items mentioned above before Slade leaves the bathroom. The missing vial won't be noticed, other missing items will generally be bad for Tex.
I suggest using the keyboard to move through this sequence, I find it quicker than the mouse.