This question covers a lot of topics so this answer may be long.
First things first, as long as the post is readable there is no reason for downvoting or deleting based on the type of formatting alone. Readable means:
the text is generally legible
(some handwritings can be terrible but if it can reasonably connected to an intended meaning, it is okay)
images are unambiguous
(‘wrong’ electron-pushing arrows are okay as long as there is only one sensible way to push the arrows correctly — however, this should be indicated in a comment. Wrong structures are also okay if the error can reasonably attributed to oversight; e.g. a missing atom description if it is present before or after)
the image is upright so desktop users don’t have to rotate their monitors
the important parts are sufficiently lit to be legible
(kind of covered by the first two points)
there is not too much irrelevant, distracting garbage on the image
needless to say, the image in general should be safe for work, not contain insults or sexual language etc.
If an image along these guidelines is given, vote/comment/answer/flag as you would if the ideal case had happened. So for example if it is an image of a textbook exercise and OP has done nothing, downvote and flag/vote to close as homework. If OP has answered a mechanism question correctly, upvote. And so on and so forth.
If, however, any of these is not fulfilled or there are other reasons why one would consider the post unreadable, please vote/flag to close a corresponding question as unclear, or flag an answer as very low quality, along with a comment explaining your action. You may choose to add a downvote; I am not sure if it is strictly necessary.
We should make sure that all images are uploaded to the Stack Exchange Imgur, i.e. have a URL starting with i.sstatic.net. OPs sometimes do not do this and then their images may be eligible for automatic deletion by Imgur, which is out of our hands. Thus, any non-SE-Imgur images should be uploaded to the dedicated SE Imgur by an appropriate edit unless you decide to reformat the post entirely as per the remainder of this answer.
All that follows here is optional and should be performed by users who are willing to put in the time and effort involved. However, partially doing this is okay if no information is lost.
In the long run, we would enjoy all schemes to be well-drawn computer images by a drawing program such as ChemSketch, all text to be written out and all tables (where reasonable) to be written out in MathJax. Graphs should also ideally be created in a beautiful way, e.g. by using Gnuplot. Orbitals and orbital schemes are a bit harder to get done perfectly and to the best of my knowledge there are no dedicated programs except for those used to perform quantum chemistry calculations. However, if you have access to a way to draw orbitals well or are willing to invest the time to do so, please feel free.
So for any ‘bad’ image, we may elect to do any or all of the following:
type out text by using MathJax where applicable and correcting any obvious typos found; with a [sic!] if need be
crop to or draw out (with ChemSketch or others) schemes and structures so that they can be used where needed
type out tables in MathJax using \begin{array} and \end{array} (This can take time if you are not used to doing it!)
crop to or redraw (with Gnuplot or others) graphs using well-chosen axis scaling and labels as well as screen-friendly and printer-friendly colours.
This list has been ordered in decreasing importance. It is more important to have actual text rather than an image for searchability. It is very unimportant to redraw the graphs as the key information can usually be read in any rendering. However, nobody should feel scared to do all of this if they wish.
