"This is the watch I had lost."
Translation:Dette er uret jeg havde mistet.
You could say: "Det her er uret jeg havde mistet."
“Der” can only be used as subject of the relative clause. In this sentence, the relative pronoun is the direct object with “jeg”as subject. Therefore, you have to use “som”, which is accepted as correct answer.
That doesn't really work. I'll try to explain a bit.
In this sentence you have subject (dette), predicative (er), object (uret), and descriptor (jeg havde mistet), in that order. I have the feeling you tried to use "detter er uret" as the object, which would warrant a swap of jeg and havde to have the predicative in the second position, but that doesn't work out, since an object can't contain an inflected verb. You could, however, say "Dette ur havde jeg mistet" - I had lost this watch, but this is grammatically different.
Tusind tak! So most of Danish sentences doesn't use verb-subject inversions as much as German?
Phew. Large parts of Danish grammar reside somewhere between German and English, so let's make some comparisons.
In main clauses of statements (sentences which are not questions or orders) in both German and Danish, you always try to have the predicative (the inflected verb) at the second position: "Jeg tog til byen i dag" - "Ich ging heute in die Stadt" or "I dag tog jeg til byen" - "Heute ging ich in die Stadt." That doesn't work comfortably in English where the predicative is mostly right after the subject: "I went to the city today" and "Today I went to the city."
If you have more than one verb in your sentence, for instance through auxiliaries or composite tenses, Danish and English try to put them all together, whereas German puts the non-predicative at the end of the sentences.
"I have seen some cats on my way this morning" - "Jeg har set nogle katte på min vej i morges", but "Ich habe ein paar Katzen auf dem Weg heute Morgen gesehen."
In the sentence discussed here, you have an attributive addition that makes sense in English and Danish, but doesn't work in German. "This is the watch I had lost" and "Dette er uret jeg havde mistet", but for the German translation you need to introduce a proper subordinate clause: "Dies ist die Uhr, die ich verloren hatte.", which is better simulated by putting 'that' or 'som' in front of the English and Danish clauses, respectively.
I hope this is what you were asking about. Giving a full overview of verb behaviour in those languages would take a while of research. xD