I am attempting to convert my late '80's Fuji Palisade to a fixed gear. The dropout spacing is 135 mm and my LBS told me that is too wide and I would need spacers to compensate for the difference. I am planning on buying a ready made wheel with a flip flop hub.

Where do the spacers go and what do they do? Is that the only way to correct for the wide spacing of the dropouts?

Also, what are the different types of bottom brackets? Will a different bottom bracket solve the problem of improper chain line due to the wide dropout spacing?

I think this is the only problem standing in the way of my conversion.

Is it a steel bike? If so you could cold-set the rear spacing on the frame. Sheldonbrown has a tutorial on how. I did this to my frame, worked well.

First question, does it have vertical dropouts? If the answer is yes, then don't bother, it's too much of a hassle.

It is a steel frame and it has horizontal dropouts. I know the conversion is possible, I'm just not sure how best to set it up. I am hesitant to bend or flex the frame because this adds unnecessary stresses on the steel and fixed gear riding is already very hard on a bicycle frame. Any more stress and things might start to go bad.

The spacers' width depend on the hub you will be using.
If the hub has a 120mm spacing then you will need spacers that add will add up to 135mm...which I don't have much idea on how will it work out; you will most likely need a longer axle as well, ask your LBS about them.
As for the chainline, a longer bottom bracket length will compensate for the spacing at your rear wheel.
Here's a list.

OK. Most rear flip/flop hubs come with axles long enough to fit up to 130mm dropouts. Typically, they come spaced for 120mm dropouts, and you add spacers on each side of the hub on the axle to space them out to up to 130mm. The problem is that your dropouts are spaced at 135mm, so you need a longer axle. So either you need to find a wheel with a long enough axle or you need to replace the axle with a longer one. The alternative is to cold set your frame by 5mm, so that it becomes 130mm dropout spacing. That is 2.5mm per side, which is not a lot for a steel frame. You can do it or a shop can do it.

Ah, ok. I think I will take this bike into the shop for some advice. This isn't quite as simple as fixed gear bikes are rumored to be...

I've cold set a few old steel frames with no problems. have no fear.

are you sure it's 135? what did you use to measure? did you measure to the inside or the outside of the frame?

the reason i ask is that, correct me if i'm wrong, but the Fuji Palisade was a road bike (the name is now used for hybrids, but that wasn't the case in the 80's). old road bikes have either 126 spacing or 130. how many speeds are on your rear cassette? (if it's original) if it's 6 or 7 then your frame should be a 126 spacing. if it's 8 or more (which i highly doubt in the 80's) then it would be a 130.