music / trouble / gnat
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music
Colloquial expression for music. Used especially in youth language and informal contexts.
Lass uns am Wochenende auf ein Konzert gehen und gute Mucke hören.
Let's go to a concert on the weekend and listen to some good music.
You can recognize the meaning of 'Mucke(n)' from the context. If it is about listening, it means music. If it appears in the plural with the verb 'machen' (to make/do), it is about problems. If it is about a single animal, it means an insect.
Mach mal die Mucke leiser, ich kann nicht telefonieren!
Turn the music down a bit, I can't talk on the phone!
The expression 'Mucke' (music) is purely colloquial and youth language. It is not used in formal situations or in written correspondence.
Was für Mucke hörst du am liebsten?
What kind of music do you like listening to most?
The meaning 'Probleme' (problems) or 'Launen' (moods) is used almost exclusively in the fixed expression 'Mucken machen' (to act up / cause trouble). Here the word is always in the plural.
Das Auto macht schon wieder Mucken, es springt nicht an.
The car is acting up again; it won't start.
The meaning 'Insekt' (insect) is rare today and more regional or old-fashioned. In most parts of Germany, people would say 'Mücke' (mosquito/gnat) or 'Fliege' (fly).
Ich habe eine Mucke im Zimmer, die mich nicht schlafen lässt.
There is a gnat in my room that won't let me sleep.
problem
'das Problem' and 'Mucken' can both describe something not working properly or causing difficulties. 'Problem' is neutral and general. You can use it for people, devices, plans, or tasks. 'Mucken' is usually used in the phrase 'Mucken machen' (to act up). It sounds colloquial and often means that a device suddenly is not working properly or that someone is behaving stubbornly. So 'Problem' fits in almost any context. 'Mucken machen' fits better in casual conversations when something unexpectedly causes trouble.
Beim Frühstück macht die Kaffeemaschine wieder Mucken.
At breakfast, the coffee machine is acting up again.
Der Fahrer meldet ein Problem mit dem Bus, deshalb kommt er später.
The driver reports a problem with the bus, so he will arrive later.