What can cause a false high tsh?

Not much: Any lab can have a temporary problems doing any test accurately. That is why an abnormal level should always be repeated to verify it. There are temporary causes for high TSH (resolving subacute thyroiditis), so that a 2nd TSH level done a few weeks after an abnormal one, could be normal. Subclinical hypothyroidism will have a high TSH with other thyroid levels normal, no symptoms.