You could probably get some better suggestions if you describe where your mailbox is, the layout of the lobby, are there any windows available to watch from across the street, what type of mailbox you have (open slot? lock and key?)
In any case, report this to the police immediately, and keep making reports every day your mail goes missing. It doesn't matter if the police do nothing about it. Next week you could catch the guy red handed, and it's just your word that this has been an ongoing thing, and his word that it was a one time mistake. Establish that this has been going on and on, it will be necessary in court. You will also have to report to the building owner if it is another resident, presumably you want him evicted. You also want your mail back, and this will require a search of his premises.
If you want cheap, establish as much of a pattern as you can, like when does the mailman come, what time do you eventually check and find your mail missing, are there any neighbours you are friendly with who are home during the day and get their mail at a specific time, etc.
Then take a couple days off, and stake out the place discreetly on your own. Have a digital camera in hand to get proof, or at least something to back you up. If you can't find a discreet place to sit all day, at least casually walk by your mail box every half hour or so and determine a time when it goes empty.
If there is somewhere you can hide out of sight, but within earshot, duct tape a small alarm inside the box and hook a string to the door so it rings when the the box opens. Then step out of hiding (stairwell, whatever, read a book) and take your picture.