I agree that you do not need to be a better writer or have a string of hits before you are qualified to critique.....just like you do not need to be a Michelin star chef to pass judgement on food......you either like a thing or you do not....and you probably know why you like it or if you did not can give suggestions as to how it could be improved. In the days of tin pan alley new songs were given the "old grey whistle test"......they were played to the old doormen referred to as "Old Greys" because of their grey suits..... now if they picked up on a catchy tune and whistled along to it the song passed.
Actually I prefer a judgement from a lay person whose opinion I can trust than from someone who perhaps may for various reasons not quite give an accurate appraisal.

Re what to put into or leave out of a demo...well we have to first establish what the demo or worktape is for....and obviously the budget involved. Rule of thumb is a final demo should be the best quality you can get.....whilst we should keep a worktape simple just to get the song across... no point in spending time and money on something that may be ditched or dramatically changed.....
Any pro studio or decent software program records in a non destructive way so that parts can be edited and cut and diced or adjusted or revisited even after the final mix cause all tracks are separate and all edits and edit history etc can be done or undone at any stage.....eg a vocal or part of it can be stripped out and replaced or another guitar part added etc and all balances and volumes altered etc...it is difficult to do that with some of the bottom end of the market ways of recording.....Bearing that in mind it is a good idea to state at what stage the song is when asking for a critique.....and whether a song is a draft work tape yet unfinished or a finished demo.