There are risks and rewards from any type of dental treatment.  The most common side effect of High Speed Braces is straighter teeth!  Potential problems or complications with HSB are the same as traditional orthodontics which may include a small chance of occurance of any of the following:

1) Sensitive teeth
It's common to have some tenderness in the teeth due to the slight pressure of the wire which stimulates the tooth movement.  It generally disappears after a few days.

2) Sore cheeks and lips
The mouth can take a little time to toughen up to the slight irregularities of the orthodontic brackets and wires.  Using ortho wax can greatly reduce this problem.

3) Pulp damage
The nerve of the tooth may devitalize or in other words require a root canal is some cases.  This is more common when teeth are being moved great distances or when a person gets hit in the mouth during orthodontic care.  The teeth are more suseptible to trauma and contact sports should be avoided.

4) Root damage
In some cases the roots of the teeth may resorb/shorten to a certain degree in response to being moved. 
UPDATE: A new report just released has stated increased risks of this type of complication may occur from extended periods of orthodontic treatment. This means faster braces are SAFER.

5) Jaw joint pain
The TMJ may become irritated during orthodontic care and require additional treatment.

6) Enamel chips/cracks
During removal of brackets there is a small chance slight cracks may develop but they rarely require treatment.  This is more common with certain porcelain brackets.

7) Relapse
If the retainer is not worn after treatment is completed the teeth have a greater chance of moving back into a less straight position.

8) Decalcification
Poor brushing and flossing habits and extended treatment times increase the chance that the enamel will get weakened by the process. Note: If the patient is a poor brusher a shorter treatment time reduces this risk.