You're right about edge cases in terms of input values, and right about issues with concurrency, but many of the issues you mention are solved by changing your metric.

Branch-level coverage tells you what percentage of codepaths are covered.

In other words, it would report 50% coverage for:

    if a:
        print "a yes"
    else:
        print "a no"
    if b:
        print "b yes"
    else:
        print "b no"

    test 1: a = false, b = false
    test 2: a = true, b = true