Sherlock doesn't actually use Deductive Reasoning:

He uses what's called Abductive Reasoning. This is definitely reinforced in the books as he's a huge "trivia" buff and reads through very odd compilations of forensic facts so he can create correlations between previously acquired data and a current situation.

By definition, this means he'll be wrong based only on the reliability of his data and his memory application. This is why he always has a few theories and doesn't say anything about which one he prefers until he's pretty sure that's the right one.

The main source of his data is actually previous crimes which have been successfully solved so that's why he manages to be so accurate in general. He has that data set as a guide.

TL;DR Holmes isn't a deductive reasoning machine, he's a database (abductive reasoning) with a really good lookup algorithm and simple, first order logic.

More Reddit comments:

http://reddit.com/r/videos/comments/25fmja/sherlock_holmes_sucks_at_deduction/

TBS has to keep Pete Holmes going. 

I hope so. Also I never realized Pete and Sherlock have the same last name.