I have done a lot of testing, and also a lot of research on the TinyMCE site, and also by going through piles of tickets at trac.wordpress.org regarding the new editor and have found out how to keep paragraph formatting.
When you start a new post, make certain that in the format pulldown (left end of lower visual toolbar) says "Paragraph." If it does, then in every browser I have tried, the editor will keep the paragraph formatting with blank lines between paragraphs.
The blockquote, unordered list (bulleted) and ordered list (numbered) functions now have to be toggled on and off via the buttons in the toolbar.
Entering a list
1. click on ordered or unordered list to start the list
2. enter all the list items
3. when done, hit return/enter (like you are going to add another item to the list) and then click on the toolbar list button to end the list
If you follow the above with lists, when you hit the list button to end the list, the editor will automatically switch back to paragraph formatting.
It's the same with blockquote
1. click on blockquote button
2. enter the quoted material
3. when done, hit return/enter one more time and then click on the blockquote button to exit the blockquote function
If you end up with paragraphs without lines between them, that means you are not in paragraph formatting. Select the paragraphs that are not formatted properly and then select "Paragraph" from the format pulldown (left end of lower visual toolbar) and the paragraphs will be formatted with paragraph breaks.
Always keep an eye on the format pulldown as it will indicate how formatting is set in the editor. When doing blockquotes and ordered and unordered lists it will indicated "format."
The bottom status bar on the editor also indicates how things are set:
Blockquote: Path: blockquote » p
Unordered list: Path: p » ul » li
Ordered list: Path: p » ol » li
If you see "Path: p » div," you are not in paragraph format and will not get blank lines between paragraphs
In paragraph format mode, you will see "Path: p."