For the red dot observations, I believe this things have been measured by at least 3 of the 4 devices on board - NIRCam (near infrared camera, has very limited spectral capabilities through its filter wheel), NIRSpec (near infrared spectrograph) and MIRI (mid infrared instrument).
I cannot pretend to have the actual expertise, but it does seem vanishingly unlikely that all 3 instruments could create consistent artefacts in the same location.
But I'm pretty sure they thought of all of this and many more objections already. It's not like this is a super advanced thread of skepticism that physicists would have overlooked
In Hubble, that fuzz was marked. With Webb, far less so.
I think these are real true positives
We can trust what we see. We can't trust there's nothing where we don't see anything.
I vouched for your two posts in this thread, but that never works, and honestly it gets a little old trying to pick up the slack left by HN's inscrutable, unaccountable, and largely-broken filter. This has been happening a lot lately, unfortunately.
Messing up the data analysis has major precedents. If you aren't familiar you should look into BICEP data in 2014, they thought they had observed primordial gravitational waves which would have been earth shattering. Instead they just messed up the dust correction pipeline. I don't envy the day they came to that realization. I was in several conference rooms at Princeton where BICEP people presented their analysis and David Spergel (of WMAP, previous head of the department at princeton) and others were able to walk them through how they thought they had kind of messed things up. This is what routinely happens, ESPECIALLY when something unexpected is observed. Every possible explanation is looked into, and ESPECIALLY in cosmology, you can do that incredibly well. Cosmology is one of the most beautiful sciences in my experience, precisely because we have such good ways to model the observations to probe various models, and you can treat the observations with Bayesian stats with virtually no risk of misspecifying your model, or, if you do find its misspecified, you have discovered something new about the universe.
The process to go from raw observations to physics, correcting for all the crap in between early universe light and us (dust which also rotates light polarization -- this explained the BICEP issue, instrument systematics which are measured to incredible precision on the ground (e.g. point spread function -- what is the detector response to various intensities of light; e.g. you get electrons for bright sources that spill into neighboring pixels)
Everyone everywhere is looking to make a name for themselves by discovering the discrepancy -- be it a screwup of some other team (astro community is generally very supportive and positive but also competitive) or a problem with simulation assumptions, a genuine discrepancy in our understanding of the universe (i.e. the tension in the hubble constant -- you infer rate of expansion from cosmic background radiation / early universe observations, and then try it using an alternative method -- using local variable stars, and you get a statistically significant difference).
So I would say: if there's a screwup it will be found, and a genuine fuckup is possible and does happen, but when it does believe me we will know usually within a few months. You'll have a ton of people trying to reproduce the results, pouring over everything there is that could possibly explain these observations. The wheel of astrophysics grinds slowly but it grinds finely.
Edit: also shoutout to Jenny Greene -- one of the world's foremost experts on galactic astronomy and also a genuinely great person. She rented me her house for a summer for dirt cheap when I was a poor grad student with nowhere to stay. Also hosted the best graduate student parties (our idea of a party is beer and board games and complaining about our advisers)