The short answer is "yes" but I bet that was not really what you were hoping for. You can look up danish words on http://ordnet.dk.
For the different meanings of the words these synonymes are mentioned:
Generally: dirty, filthy: snavset, smudsig
1.a of that which may make you dirty
1.b indecent, treacherous, criminal - lousy, common: tarvelig, gemen
1.c about work - harsh, hard, trivial: ubehagelig, hård, triviel
1.d about language - foul: sjofelt
1.e about music - noisy, rough, unpolished: larmende, rå, upoleret
I can come up with a couple of related words some of which are probably in the slang category:
namset (gooy), nasset (sticky), ulækker (disgusting), klam (damp, clammy), ækel (vile), uhygiejnisk (unhygienic), forurenet (contaminated), uren (unclean).
If the adjective was used as an attribute, you would be right: "Den beskidte jakke". But in this case the adjective is a predicate: "Jakken er beskidt". In English the adjective has the same form in both cases: "The dirty jacket" and "The jacket is dirty". That's just not the case in Danish. I hope that helps. Forgive me if I messed up some of the grammatical terms. I just realised that I've used the word "case" three times.