I only use notebooks in R (via knitr). Unless you choose to cache specific blocks by flagging it, it re-runs the whole notebook from scratch every time... So personally I haven't had any of these problems before. Further, the rendering is static, so you can't really choose to run things out of order either.
If you use notebooks inside R-Studio (like I imagine 99% would do) you click ctr+enter inside a code block and that block and only that block is executed, and below, the output of that block is rendered.
Absolutely don’t :)
Emacs + ESS all the way .