Over what range do Thyroid Stimulating Hormone (TSH) levels tend to fluctuate over the course of a day?
I wrote an answer about the circadian rhythm of TSH for a question over on Health.SE: How does one's TSH tend to vary over the course of a day. That answer also has some information on how this is different in people with hyperthyroidism and hypothyroidism. 

The paper Physiological variations in thyroid hormones: physiological and pathophysiological considerations has a section on circadian and seasonal rhythm and a table with some values. Quoting from the paper:


  There is a clear circadian variation in circulating TSH concentrations in animals and in humans. TSH concentrations are low during the daytime, increase in the evening, and peak shortly before sleep.  Amounts decline slowly during sleep. Table 3 summarizes studies of mean, nadir, and peak serum 


This is table 3:



A chart is available in figure 2 of the paper Modulation of Endocrine Function by Sleep-Wake Homeostasis and Circadian Rhythmicity

As for test error, it's important to note that TSH itself is not used for or at least should not be used for diagnosis of Hypothyroidism and hyperthyroidism. T3 and especially T4 need to be measured.