As Steve suggests sensible levels of use shouldn't cause any great issues. One common issue is CTS (Carpel Tunnel Syndrome). Easily negated by lowering the dose.
In rare examples (from Perimeter Institutes website)
Insulin resistant diabetes
Changes in bone structure
Enlarged or inflamed organs, especially the pancreas
Sleep disorders
Carpal tunnel syndrome
Increased cranial pressure
Bleeding
Growth of internal organs leading to what is known as HGH Gut
The appearance of moles on the skin
High HGH levels could cause Gynomastia which means basically Breast growth in males
Cancer that might take years to grow could with HGH spread much faster thus shortening the life expectancy of the sufferer