When I worked at my last position someone always remarked about the state of the Dutch language and how it is slowly degrading. Some people I talk with remark about the misuse of hun (their, them – when it’s a indirect object) vs. hen (them – when it’s an direct object).
And what are direct and indirect objects again?
Ik gaf het aan haar. I gave it to her.
het = direct object
haar = indirect object
Thus you can see a sentence like this:
Ik heb _____ gezien. (you are filling in the direct object)
hen = correct (for persons only)
hun = not correct, but often heard
ze = used for persons OR things
So what do we use hun for again? Possession of items.
Ik heb hun fiets gezien. I have seen their bike.
And what about prepositions? Because we all know those are just made to complicate things…
When preceded by a preposition, use hen (door hen, aan hen, voor hen).
And how did I get to the B2 level without realizing this?
As mentioned above, the unmarked/unstressed form for direct objects is ze. Thus: Ik heb ze gezien. is acceptable provided you are not emphasizing ‘them’.
If you can read Dutch, this is a very fun article to read. Kofschip op de klippen. It’s about a Dutch family which moved to the US, with the mother realizing that the children’s Dutch was being taken over by English phrases. Opening example: Ik heb de team gemaakt. (English – I made the team). Better Dutch: Ik wordt gekozen voor het team. I have been chosen for the team. (Note January 2016: it should be Ik word gekozen… the t was a typo.)
Life in the Hague 
Just a brief comment to the second last sentence:
Even better Dutch: “Ik word gekozen”
Ooh, nice catch. Thanks!
And wow, that was a year and a half ago. Time flies when you are learning Dutch!