from what I've read, there isn't anything like a "cure time" found with other glues — as soon as the two sides make contact, and pressure is applied, a permanent bond is formed
Contact cement is designed specifically for adhering laminates to table tops, and for floor tiles. In these situations, there's almost no opportunity for off-gassing, so the bulk of the curing has to happen before the surface is attached.
Contact cements are famous for having extremely strong fumes[2]. There do exist contact cements that aren't as bad (known as "no VOC" versions (TODO — are either "water-based" or "non flammable" basically equivalent to "no VOC"?)). However, there are mixed reports about how good they are — some people believe no-VOC versions definitely don't work nearly as well as the traditional versions, while other people insist they work just as well. You'll have to decide that for yourself.
Not letting it dry fully — Test with your finger, it should feel slightly tacky but shouldn't stick to your finger. It should also look dull.
The glue layer ends up too thin — Start with glue that has a thick consistency, and isn't runny. You can apply a second coat of contact cement before the first coat dries. Each time you apply a coat of glue, make sure it's a thick coating.
The glue is too old or has too little solvent in it — Throw out containers of old glue, where the glue has become too thick. Buy multiple small cans of cement, since contact cement doesn't start drying out until it's opened for the first time.
The surface isn't prepared properly — The surface must be clean and rough. For rubber material, first clean with methylated spirits, and then score it with a rasp or file. For leather surfaces, sand with 400 grit sandpaper until the top layer of leather is removed, then apply two coats of contact cement (the first to soak into the pores, and the second to bond to the opposite side).
Pressure isn't applied properly — Apply a lot of pressure, starting from the center and working outwards, either with a roller or a rubber mallet.
This article mentions four of the most common problems when using contact cement:
not allowing the adhesive to dry fully before assembly
waiting too long before assembly
applying too thick a coating of adhesive
not applying enough adhesive
Also, "When used on a porous or semi-porous material such as wood or plywood, a first 'priming' coat of contact adhesive may be needed to preseal the material. Otherwise, some areas may absorb too much adhesive to form a strong bond. This prime coat is followed by a second gluing coat. Following the label directions concerning drying times, application thickness, and using the proper tools."
TODO — what are the SOLUTIONS to those above "four common problems"? Unfortunately that document doesn't mention solutions much.