Okay, to look at some of the specifics:

Superior processing power. Evidence against would be the human brain already being close to the physical limits of what is possible.

The linked article is amusing but misleading; the described 'ultimate laptop' would essentially be a nuclear explosion. The relevant physical limit is ln(2)kT energy dissipated per bit erased; in SI units at room temperature this is about 4e-21. We don't know exactly how much computation the human brain performs; middle-of-the-road estimates put it in the ballpark of 1e18 several-bit operations per second for 20 watts, which is not very many orders of magnitude short of even the theoretical limit imposed by thermodynamics, let alone whatever practical limits may arise once we take into account issues like error correction, communication latency and bandwidth, and the need for reprogrammability.

Superior serial power: Evidence against would be an inability to increase the serial power of computers anymore.

Indeed we hit this some years ago. Of course as you observe, it is impossible to prove serial speed won't start increasing again in the future; that's inherent in the problem of proving a negative. If such proof is required, then no sequence of observations whatsoever could possibly count as evidence against the Singularity.

Superior parallel power:

Of course uses can always be found for more parallel power. That's why we humans make use of it all the time, both by assigning multiple humans to a task, and increasingly by placing multiple CPU cores at the disposal of individual humans.

Improved algorithms:

Finding these is (assuming P!=NP) intrinsically difficult; humans and computers can both do it, but neither will ever be able to do it easily.

Designing new mental modules:

As for improved algorithms.

Modifiable motivation systems:

An advantage when they reduce akrasia, a disadvantage when they make you more vulnerable to wireheading.

Copyability: Evidence against would be evidence that minds cannot be effectively copied, maybe because there won't be enough computing power to run many copies.

Indeed there won't, at least initially; supercomputers don't grow on trees. Of course, computing power tends to become cheaper over time, but that does take time, so no support for hard takeoff here.

Alternatively, that copying minds would result in rapidly declining marginal returns and that the various copying advantages discussed by e.g. Hanson and Shulman aren't as big as they seem.

Matt Mahoney argues that this will indeed happen because an irreducible fraction of the knowledge of how to do a job is specific to that job.

Perfect co-operation:

Some of the more interesting AI work has been on using a virtual market economy to allocate resources between different modules within an AI program, which suggests computers and humans will be on the same playing field.

Superior communication:

Empirically, progress in communication technology between humans outpaces progress in AI, and has done so for as long as digital computers have existed.

Transfer of skills:

Addressed under copyability.

Various biases:

Hard to say, both because it's very hard to see our own biases, and because a bias that's adaptive in one situation may be maladaptive in another. But if we believe maladaptive biases run deep, such that we cannot shake them off with any confidence, then we should be all the more skeptical of our far beliefs, which are the most susceptible to bias.

Of course, there is also the fact that humans can and do tap the advantages of digital computers, both by running software on them, and in the long run potentially by uploading to digital substrate.