Bad situation, but not serious to finish up with (6)
I believe the answer is:
plight
'bad situation' is the definition.
'plight' can be an answer for 'situation' (I have seen 'Unfortunate situation' mean 'plight' so perhaps 'situation' could also mean 'plight'). I'm not certain of the 'bad' bit.
'not serious to finish up with' is the wordplay.
'not serious' becomes 'light' ('light' is the opposite to 'serious').
'to finish' means one lot of letters go next to another (some letters go after or 'finish' others).
'up with' becomes 'p' (I can't justify this - if you can you should give a lot more credence to this answer).
'light' put after 'p' is 'PLIGHT'.
'but' acts as a link.
Can you help me to learn more?
(Other definitions for plight that I've seen before include "Promise - trouble" , "Pledge; predicament" , "Dilemma" , "pickle" , "Serious predicament" .)