Trolling around YouTube brought me to this 10 minute video, which is a condensed set of highlights of Everton's 1984 - 1985 season, in which they won the old First Division and the European Cup Winner's Cup, missing out on a Treble several days later to a single goal from Manchester United.
The subsequent season saw Everton come in second in the league and the FA Cup to Liverpool. They were unable to play in the European Cup because of the ban on English teams as a result of Liverpool's fans role in the Heysel Stadium disaster.
There are some pretty impressive goals in here, especially the third goal in the home win against Bayern Munich.
One small detail that is shocking now is the fences that the supporters were behind, in the pre-Hillsborough days. There's no doubt that English stadia are safer as a result of eliminating standing terraces, but as this clip from the beginning of the Cup Winner's Cup against Bayern Munich demonstrates, there's definitely a loss in atmosphere.