can't code simple linebreaks in html editor

i’ve never had so much trouble getting linebreaks in wordpress as i am now. i’ve built sites using wp since 1.5 and am accustomed to being able to create linebreaks and blank lines in the html editor with simple carriage returns, and at most reverting to <br />. now, building a site on 3.2.1, i can’t find any way to get the simple spacing i’m after… and the mark-up created by wordpress is bizarrely bad. </p> that have never been opened, and broken nesting (though i’ve checked that settings box instructing WP to automatically correct poorly nested tags).

the html editor doesn’t show the actual html that will be used to render the text, and strips out html i insert in favor of garbled mark-up. it’s frustrating not to be able to at the very least code a linebreak.

i see other threads on this topic, but haven’t found any clear answer or explanation as to how WordPress can be so bad at something so simple.

really hoping someone will point out something that i’m doing wrong or haven’t thought of. the thought that wp really is so flawed is depressing.

the site i’m building is here:
https://synthesis-in-action.com/

in particular, the section under ‘what our clients say’ has a closing </p> without an opening, and an opening without a closing. and i’m trying, without luck, to get a linebreak between the author of the quote and the company he works for. i’ve tried coding a <br /> in the obvious place, but the editor (yes, using the html editor, and have tried disabling the visual editor) strips it out.

any ideas?