The chief effect is a simple one, many users load several pages from the 'latest posts' links and may not read them until later without realising further posts may have been added. This can affect anyone and isn't as severe as what we used to suffer in the days of 'off line readers' (OLR lag).
When you get a really big change, it usually means you have clicked on a link on the latest posts list or the latest posts page that was generated some time ago. If the list is a couple of hours old because you haven't refreshed it AND you have it set to 'go to latest page' it will take you to the latest page for when the list was generated. If the topic has since gotten a page longer, you may not notice the link to the extra page and not see the extra postings until you post your own message.
There are also occasional glitches that mean a user's posts get stuck in the system for a while. As Jason says only a few topics are pre-moderated as well as new members early postings.
Neil