I had new ceramic tile flooring layed in the front room and because the floor was so uneven putting on the baseboard is a struggle to make it look straight. Is there a way to cut the baseboard when the floor is even the first 4' and has a 1" drop in the next 4'? How do I make it look straight?

 

You'd have to start at the lowest point and scribe the bottom of the baseboard to match the floor. The top of the baseboard would theoretically be level. So if it helps, find your lowest point, put a level line on the wall, and measure down.

Scribing to a crooked floor is tedious work, but that's what it takes sometimes.

 

Consider the corners, what will happen if you cut the bottom off of one side and not the others? If it will work then do as xsleeper suggested. If it won't work without cutting all the sides different sizes then consider putting the molding straight and use your shoe molding to hide the gap.

 

Shoe mould is the easier way to go but unless I'm mistaken, shoe moulding is only 3/4" high which won't hide a 1" gap

It would however allow you to get by with less trimming off of the bottom of the base. It would also hide any less than perfect cuts