Make sure your mailbox is labeled really clearly with your name and apt number. According to the website, the letters should be 1" tall. I also posted below that if you have a mail cubby (with a door and key) you need to make sure your name and apt number are visible INSIDE the cubby. Your mailman doesn't have a key to each box, he has one key that opens all the doors at the same as one big door. The little door with the number is for your benefit- it does your mailman absolutely no good at all. http://www.usps.com/receive/mailboxstandards.htm
I'm not sure what kind of apt you live in.
A multi-family apt bldg:
You might try adding a bin on the floor below the mailboxes with a note on your mailbox that says something along the lines of "If a parcel does not fit, please leave in the bin below". When I lived in an apt with 6 small mailboxes on the wall and it absolutely would not fit, they often left it on the floor below the mailboxes (or since i lived on the groundfloor and my door was across from the mailboxes, they would leave it in my doorway).
A large apt complex: If you live in a complex where there's about 25-50 mail cubicles with a key to open them on the wall and the mailman swings open a door for immediate access to all of them, you might try writing a note to the mailman (My mail is being returned to sender and I'm not receiving any hold mail notices to pick items up at the post office yada yada yada) and taping it facing out in your mail square. Also- VERY IMPORTANT: Make sure your name and apt number is visible inside your cubby because the numbers on the metal doors aren't visible when they put the mail in your box. If there's no name and no apt number, it's just an empty box- considered vacant/unoccupied or nonexistant. Yes, your mailman could use process of elimination from the boxes on either side of yours to determine your box, but that doesn't mean they will, and if you have more than one mailman, one might deliver your mail and another might treat it as undeliverable. I would also try checking the main office of a mass complex to see if they have any mail for you. When i lived in a 4 building complex, mail that didn't fit usually went to the main office and the main office would leave a note in our box. Your building may do the same thing but not go to the trouble of leaving notes- find out if your mail goes to an office or not.
Also, everywhere that I've lived except my childhood home has had more than one mailman with the same route throughout the week (example: my landlord waited a few days to shovel the walkway from their house to the back where our house is. joe shmo will walk back to our house anyway, but jack black who does the route every other day will not so i got my mail on thursday and saturday, but not on friday) which may be why you get some of your packages but not all of them.
If expected First Class Mail or Priority Mail has not arrived within 5 postal business days from its date of mailing, you can:
§Call 1-800-ASK-USPS (1-800-275-8777) where a customer service representative will document your concern, OR
§Visit the Postal Inspection Service websiteand complete a mail loss report.