Reflections could definitely distort results but I would expect those errors to be more obvious.
Flare could be coming from several sources in this test setup. First there's the bright area around the transmission tablet. There are several ways of reducing this effect, such as surrounding the tablet with black paper, or masking the lens or masking the camera or combinations of these.
Then there's the fact using a backlit transmission tablet (or a front-lit reflection tablet) will put some degree of flare into the test anyway. As long as you are using a wedge/tablet (ie a wide range of adjacent "luminance values" in a single frame), there is no way to eliminate that kind of veiling flare other than contacting the wedge, which is the no-flare method Stephen refers to.
The problem is to balance the factors and make sure the test is meaningful. For example, in order to generate the "purest" possible (let's call it "native") comparitive curves of different films in some sort of standardized way, contacting is useful because it removes flare from the tests. However, to then evaluate a film in the context of the actual photography you will be doing, it always seems to me contacting is too far removed from actual conditions to give you an accurate picture of what the film is doing - unless you typically photograph under low-flare conditions. Depending on flare, speed can change, as can contrast particularly in the low densities (ie shadow values). Of course speed and toe contrast are interrelated. Flare flattens local contrast in the low densities.
I keep meaning to post the curve results of a comparison (flare/no flare) test to the other thread I started recently regarding flare, but I just haven't had the chance. Hopefully this weekend.