(Updated)
I think your interpretation of "if I don't live in a simulation, then a fraction x of all humans lives in a simulation" as P(SIM or A) is wrong; it makes more sense to interpret it as P(A|¬SIM). This actually makes the proof simpler: for any A, B, we have that P(A) ≤ P(A|B)/P(B|A) by Bayes theorem, so if we accept that P(¬SIM|A) = (1-x), then we have P(¬SIM) ≤ (1-x)/P(A|¬SIM).
I think your interpretation of "if I don't live in a simulation, then a fraction x of all humans lives in a simulation" as P(SIM or A) is wrong
Huh?
The paper talks about P(SIM | ¬SIM → A), which is equal to P(SIM | SIM ∨ A) because ¬SIM → A is logically equivalent to SIM ∨ A. I wrote the P(SIM | ¬SIM → A) from the paper in words as P(I live in a simulation | if I don't live in a simulation, then a fraction x of all humans lives in a simulation) and stated explicitly that the if-then was a logical implication. I didn't talk about P(SIM or A) anywhere.
Jonathan Birch recently published an interesting critique of Bostrom's simulation argument. Here's the abstract:
The paper is behind a paywall, but I have uploaded it to my shared Dropbox folder, here.
EDIT: I emailed the author and am glad to see that he's decided to participate in the discussion below.