The NMISS() and NVALID() functions could be useful here. Something like:
COMPUTE #missing = NMISS(variable list).
COMPUTE #valid = NVALID(variable list).
COMPUTE #total = #missing + #valid.
COMPUTE propmiss = #missing / #total.
VARIABLE LABELS propmiss "Missing data proportion".
DESCRIPTIVES propmiss.
SELECT IF propmiss LE .8.
DESCRIPTIVES propmiss.
Replace "variable list" with your list of variables, bearing in mind you can use the key word TO (e.g., firstvar TO lastvar). If you don't want to completely remove cases with propmiss > .8, set a filter rather than using SELECT IF.
HTH.