So, Heiwa, since you're listening, do you not agree when doing an energy balance equation that all energy needs to be taken into account?

Including potential energy. In a generalized closed orbit, total mechanical energy is a constant (for some mass, or in "specific" form with mass factored out) but it is formulated as the sum of potential and kinetic energies. One term is the "mass suspended above a planet and acted upon by gravity" term, and the other is "mass moving through space at some velocity" term. In the general case, the values of the potential and kinetic energy terms respectively fluctuate at each point along the orbit, in a ratio bounded proportionally by the eccentricity of the orbit, but their sum remains constant.

It should be noted, however, that transfer orbits are not considered closed orbits and the energy-sum conservation game isn't helpful in that formulation.

Your idea of keeping it simple involves missing out terms in the equation and getting signs wrong.

Indeed every conspiracist who attempts to impeach Apollo on technical grounds sets aside the actual working models and formulates his own simpler forms. Ostensibly, according to the proponent, this is to spare the layman reader from the tedium of complicated models, but it doesn't take much discussion to reveal that it's really to try to shoehorn the problem into the proponent's rudimentary knowledge of the relevant science. Here Anders has tried to re-invent the science of orbital mechanics from some incomplete smattering of basic physical principles, and running into the anticipated problems. Understanding specific energy as negative in some cases and positive in other cases (most appropriately, negative for closed orbits), is no problem for people who understand the concept of energy and have seen the wisdom in choosing the reference frame as we have, so that we can generalize the results to all orbits instead of orbits around some arbitrarily chosen planet. He doesn't know how orbits work, so he works out how he thinks orbits "must" work. He works an equation and the energy comes out negative, so he panics.

We saw this also in his failure to consider a rocket as a variable-mass vehicle. Which is to say, he knew that was a property of rockets, but he didn't know how to incorporate it. He wasn't aware of the Tsiolkovsky model, and his incompetence at mathematics and general physics seems to have prevented him from deriving it. So he ignores it. And he doesn't even ignore it in the traditional pseudo-science manner of assuming it's negligible. In true foaming-at-the-mouth form, he writes it off to "NASA's inability" to provide him with correct figures. He implies he'd be able to account for it properly if only NASA hadn't been so secretive, but then proceeds to ignore its effect entirely and insinuate that his known-inaccurate figure is somehow irrefutable proof of a hoax.