I had received notifications that I let pass a "possible smuggler". But for me is not really clear how to detect smugglers in Papers, Please, could you help?
Primarily you should be looking for a variance between the weight shown on the scales when a prospective entrant steps into your booth, and the weight listed on the entrant's ID supplement, Access Permit, Identity Card or Grant of Asylum.
If the listed weight differs from the actual weight of the entrant, you can raise this as a discrepancy, and the resulting interview will provide you with the opportunity to scan the entrant with your X-ray.
Contraband will be visible on the (rather depressing) photo - often strapped to the entrant's back, chest or legs - as a distinctive black block or smudge. You can then raise a discrepancy between the contraband on the photo and the 'No weapons or contraband' rule in your rulebook; the entrant should then be 'removed' from your booth by a guard, and you can proceed with your duties.
Glory to Arstotska.
(Sources: Personal gameplay, http://papersplease.wikia.com/wiki/Contraband)
Once you receive the notification that you should stop smugglers, you'll also gain access to the x-ray machine. Any attempt to introduce smuggled goods in the glorious Republic of Arstotzka will show up in the x-rays picture you get from the machine, also showing any cross-gender attempt to fool you.