Every diagnostic assay has a certain level of variability associated with the test. It's known as the reproducibility of the assay and it indicates how the results of the same sample repeat over time. There are all sorts of things that affect the reproducibility of an assay. Generally, the variability of an assay is determined during clinical trials of the product before it goes on the market and is part of the information in the package insert of the test kit.
Reproducibility is calculated by taking the same sample and testing multiple replicates of that sample on a single run, on multiple runs each day, over multiple days, by multiple techs, in multiple labs, and on multiple lots of reagents. Any quantitative test (a test where the result is a number) has a known variability. It's possible that the two results you were given are within the known variability of the assay. It's also possible that there was a slight difference in the two samples you provided. I'd be more interested in the time of day they were drawn in relation to each other than the fact that it was Wednesday vs Thursday. The difference could very well be morning vs afternoon and how your thyroid function changes slightly throughout the day.
Yes, I would keep the appt with the endocrinologist. He'll probably suggest repeating the tests again to get a better feel for your current state and the suggestion to recheck the levels periodically will probably be repeated.
Phoenix and Roger --- that's a very common observation. Probably, as Roger says, to slight changes in lifestyle once the first diagnosis is made.