What side effects can I produce if I take thyroid hormones to lose weight?

Worst case? Stroke. The amount of thyroid hormone that would need to be taken to induce a significant weight loss can predispose to type of heartbeat irregularity called atrial fibrillation which can lead to a stroke. It can also cause osteoporosis which increases the risk of fractures.
Lots. Dangerous stress on your heart, irregular heart rhythms, loose stools, sweating, heat intolerance, and thinning of your bones. Medical drs do no recommend this approach to weight loss. It is dangerous and not sustainable - you'd likely regain a lot of weight once you stopped the med.
Weight GAIN. Many people with thyroid hormone levels above normal actually gain weight. Although their metabolic rate is increased, their appetite is also increased and will power/impulse control is zero. They may burn 100-200 extra calories a day, but eat 500-1000 more calories a day, and thus gain weight. This is especially true for people with weight problems to begin with.
Lots. Including anxiety, heart problems, insomnia and more. It is not a safe or effective means of long term weight loss. To lose weight and keep it off you need to change diet and lifestyle habits for the rest of your life. A program that cannot be maintained indefinitely is unlikely to result in sustained long term weight loss. Weight watchers is one of the best programs out there.
Re: TSH. In response to dr. Treacy's answer, the TSH remains the most reliable test for thyroid hormone abnormalities. It is the hormone from the pituitary that tells your thyroid to work. It responds to your body's thyroid hormone levels. The only instance in which it cannot be relied upon is in people with a non-functioning pituitary gland.
Several. As answered, too much thyroid hormone can produce bone loss & heart irregularities. However, most patients who are low in thyroid are underrecognized. The TSH is a poor screening test for thyroid function. The full thyroid panel is needed to assess optimized thyroid function. More than 50% of patients in my practice are low in thyroid hormone levels past age 40.

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