Continuity mistake: When Homer is climbing the dome, there is a shot of the rope. No-one is climbing it, yet a few seconds before people were climbing the rope. (01:05:10)
Suggested correction: They didn't climb high enough to be visible. Homer was much higher than they were.
Character mistake: The mob is marching to Homer, however they are going the wrong way. In the mob we see several people who all know where Homer lives. So why march the other way? (00:31:40)