Does pooling rainwater pose a threat to my roof?
There are situations where water pooling on a flat roof is a problem, but this probably isn't one of them.
The cases where it's a problem are where water pools, the weight of the water deforms the roof structure, so more water pools, so the roof deforms more and collapse results.
You appear to have a relatively small area of poorly graded surface near the drain, which is unfortunate and poor quality work, but not particularly threatening to the integrity of the roof. Correcting it would be a matter of fixing the level of the underlying foam surface and waterproofing over that corrected surface with the materials that the roof is made from (unless re-doing the entire roof).
While unsightly, the collection of some dirt and debris is not a concern for the health of the roof. Holes drilled into the surface might be, however.