When Johnny Depp and Christina Ricci are riding back into town you can see a barbed wire fence in the background. Barbed wire wasn't invented until the 1800's and wasn't invented anywhere near Sleepy Hollow.
with a bit of research, it seems that barbed wire was PATENTED May of 1873. But it is stated that several other types of barbed wire were created before 1865. Sleepy Hallow is supposed to be taking place in about 1799 (Ichabod makes a comment about the new millenia). So according to my research, not to sound like DA from magic school bus, its not likely that barbed wire would have popular enough to use at that time let alone even invented yet. I think this could count as a slipup. not a big one, but one none the less.