Jeffrey and Phineas don't carry any luggage, but every time they return from a time travel related costume change they both are back to wearing their original clothes.
Although Charles Dickens did base his character Fagin on the real-life Ikey Solomon, no actual Fagin, Bill Sikes, Nancy or the Artful Dodger exist in history.
The establishing shot of Washington shows the US Capitol with a complete dome, however, the current dome was under construction throughout 1863, only completed in December. There should have been scaffolding around it.
A boom mic is briefly visible when Bogg and Jeffrey first meet Marion Brownlow in the market.