A plothole you could drive the Hong Kong Cavaliers tourbus through
As I understand the plot (which admittedly is not as thoroughly as true fans), back in 1938, Drs. Lizardo and Hikita invent an oscillation overthruster, which allows Lizardo to partially go into the Eighth Dimension. As a result, Lord Whorfin escapes from imprisonment there and inhabits Lizardo's body. Meanwhile, because of this rift, 46 other Red Lectroids escape into the Eighth Dimension. (Oh, god, I can't believe I'm seriously analyzing the plot of this movie.)
Because of his dual personality, Lizardo goes "insane," and kills someone, gets caught, then gets put into the jail for the criminally insane, where he spends the next 45 years or so.
Although the oscillation overthruster Lizardo/Whorfin built while imprisoned didn't work, I think this had to be due to a lack of proper materials, and not due to any lack of knowledge.
In any case, why would the Red Lectroids found Yoyodyne, with its fat defense contracts, and not spring their leader, keep him safely hidden inside Yoyodyne's plant (where no human had ever set foot before), allow him to work on the overthruster with all the money that a padded defense contract could allow, and get the hell outta there, and back to the Eighth Dimension? It seems like that could have been done in a lot less than 45 years.
And what was it about Buckaroo's going into the Eighth Dimension that all of a sudden inspires Lizardo/Whorfin's escape to Yoyodyne? Again, why not do so 45 years earlier?
I asked the doctor to take your picture so I can look at you from inside as well.