We always accept both de and dom, but we use de as the default. But it should really be the other way around - since there is a bug with "type what you hear" exercises, which causes only de but not dom to be accepted.
Do you happen to remember what the sentence was, so I can check it?
This isn't quite right. Let's explain it this way instead:
den and det both mean 'it', depending on gender. If you talk about 'the book', boken, you say den, but if you talk about 'the house' huset, you say det.
dem is the object form of the pronoun de which means 'they', so dem means 'them'
De tycker om det = They like it
De tycker om dem = They like them
You can hear the difference clearly in the spoken language because dem is pronounced as if it were written dom.
det is normally pronounced as if it were written de
It's just that they're talking about some object (concrete or abstract) that was previously mentioned, and since we don't know that context, we don't know what gender that object is, so both are accepted. The speaker knew what gender the object was though, so for them there was no choice.
I was typing "De tycker om dig." and instead of just saying "that's incorrect" i get the message "you've typed in english, not swedish" which is clearly not the case. This has happened on other lessons and it is really frustrating because it kind of makes me feel like I'm going crazy.
The problem is that only one accepted answer can be used for the "type what you hear" exercises, so we have to choose which one to accept, in which case de is better.
However, this has recently been fixed by Duolingo, so for the next tree version we'll finally be accepting homophones as well. :)