This is tried on both Firefox and Chromium, and I suspect this is also true in other browsers too.
This bug rears its head over at (story ID 72917) Dominion Background and Author's Guide and possibly some other articles too.
Summary of bug: The new splitting of article sometimes split it in the middle of a blockquote (or possibly similar tag) resulting in a different DOM tree than what is expected.
Details of the bug: (I'll leave out the angle brackets in the HTML tag desctiptions)
The new split of contents occurs in the middle of a blockquote, so the initial HTML received by browsers is ill-formed. The browsers then run in the quirk mode and attempt to fix this by inserting the closing /blockquote tag at the end of the parent (article) tag, resulting in everything from the div-node id="sr" to the div-node class="end-note" (plus the comment immediately after) all now wrapped inside the blockquote. Clicking it to load the second part of the content will not fix this as, AFAICT, the script put the second part of the content inside the id="sr" div so now the browser sees a stray /blockquote that it decides to remove.
The only way I can think of to fix this is to only split up after the end of a paragraph that is a child of the article and not grandchild (or further decendents). However, I don't know whether the current site backend is doing it on-demand or predetermined, but either case it will come with additional server load.