There are two main types. Those that clamp to the bike and those that fix to the bike via a socket attached to the rear wheel nut. There are also additional types specific to some trailers.
All clamps should come with some sort of restraint, so if the clamp should ever fail, then the trailer stays with the bike. The tow hitch should also allow the bike to rotate, so if your cycle should fall over with the bike trailer attached, then the trailer stays upright. (Note that the part that rotates may be quite stiff as a bike or cycle trailer can provide a lot of leverage).
Important if storage and transportation is an issue. How long does it take and what do you need to do to take it apart. What bits are you left with? Will they easily fit into the car? What else do I need to fit in the boot at the same time?
How many children do you intend to take? Do they have friends? Do they have a large teddy that goes everywhere, what do you intend to take with you (picnic etc). Are you likely to pick up any shopping? If it converts to a stroller, do you need room for the wheel etc, so you can use it when you get to your destination?
Many trailers have a frame that surrounds your child. This can provide extra protection. Is this something you desire? If so, how strong is it? If it uses hinges and brackets, how strong are these?
Bike trailers (on their own) don’t normally have brakes unless they’re the more expensive types. However, if you intend to use it as a jogger, a brake should be supplied, as this helps you control your speed when going downhill. (A jogger should be used with a safety line ‘wrist strap’. Should you trip and fall; it ensures the trailer doesn’t carry on without you – especially downhill!). Some bicycle trailers come with parking brakes (not to be confused with brakes that slow your speed). These can either be something that locks the wheel(s) or a simple strap that loops through the wheel. Therefore if you intend to use a bike trailer as a combined trailer/buggy, remember you don’t always get a parking brake as on a push chair.
Any warranty issues should be solved by the supplier. However individual parts may be hard to come by depending on the make and model? The more expensive bike trailers do normally have a ready supply of spares, but if it’s a ready built item imported into the country via China… Though this is no different to many, low cost imported items. Having said that, if you’re fairly handy, most things can be repaired, or someone can repair it for you (a bicycle trailer is not normally a complicated, specialist piece of kit).