The adhesive on regular Scotch Tape will ooze over time. Scotch 'Magic' Tape is better, but do try to get hold of some professional non ooze tape.

Draw a straight line on a sheet of plastic.
Align each side of the tape to the line and stick it down with tape so that the broken ends join up.
Put a piece of non ooze tape over the join and rub it with your fingernail so that it is firmly stuck.
Trim the tape with a razor blade or Exacto knife so that the join is very slightly thinner than the tape itself.
The join should be curved inwards slighly and should have no sharp edges.

If the cassette case itself is damaged, go and buy some cassettes at the dollar store and throw away the tape.