When Dipper and Mabel investigate the wax figure of Stan, they notice the footprints left by the killer has holes in them. However, the first set of footprints they look at doesn't have any holes.
The Sheriff says there's no fingerprints on the ax, despite the handle having been visibly handled by Soos by the register, then Mabel, then Dipper holds it with his left hand while in the bar, then the Sheriff handles it himself. Also, the security tape time shows 00:10:ss:mm so it would have been Saturday at 12:10 AM so not an alibi for 10 PM Friday night.
Mabel or Dipper handle the axe, then Soos handles the axe, then Dipper DEFINITELY handles the axe, yet Sherriff Blubs can't find ANY fingerprints on it despite 2-3 people having held it.
Toby Determined's security tape which is his alibi clearly shows the seconds in the 3rd field, then milliseconds last, meaning the 10 in the second place is minutes and the first number is hours, so the time was actually 12:10 AM, not 10 PM.
The clothing of the wax figures is shown as melting along with the "bodies"; in real wax museums the figures wear regular clothing, not garments made of wax.
Dipper and Mabel note that the wax figures have a hole in one shoe, to stabilize them on the stands. However, this would leave a raised spot in footprints the figures' shoes would make on the carpeting, not a hole.
The wax Sherlock Holmes melts almost instantly, when that much wax must take hours, if not days, to melt. Example: One birthday candle melts in 20-30 minutes.