1. In a Ask/Show HN post, (which is often similar to a reddit AMA), the OP will not be able to reply to clarifications questions until their previous one is 'endorsed'.
2. Multiple (<1000 karma) people will post very similar response to a question, or other objective comment, since they would not be aware of other pending comments on that thread. This would lead to...
2a. Either moderators endorsing multiple such comments, due to race conditions and stale views during moderation, or
2b. Moderators would endorse the first (or "best") of them, and many people with reasonable comments will be in limbo in the rest of HN, for the fault of writing a similar response to another endorsed poster.
3. (NEW) If a user has something meaningful to say to two different posts, he/she is now more likely to choose the one with more activity since he can't post on both anymore, and he/she wouldn't want to wait for the moderators to see the less active post. As a result, the power law distribution on post activity is going to become even more prominent than before.
I would recommend the following changes:
1. Apply this policy on a per-page basis, rather than on a global HN basis.
2. Allow 2 or 3 pending comments per person, rather than 1. Anyone who needs more than that, and is not getting endorsed at all, is probably trolling or spamming, and can be dealt with other means.
3. Auto-accept pending comments after 24hrs for users with >250 karma (or some other lowish number that filters out absolutely green accounts).
4. Add a "showpending" option. Even if people can't upvote/reply to them, it's democratic to be able to see them.
5. (UPDATE, adding tantalor's suggestion) #1 above can be solved by auto-accepting the OP's comments instantaneously. I would even go further and give endorser rights to the OP on a Ask/Show HN post.