Easiest answer to a worthy question first:
If a fuel quantity indicator is functioning, but the pilot suspects that it is not accurate, it really will fall to the pilot to either delcare it unserviceable, because it is not performing its intended function adequately, and document that, or, decide that he/she can defend flying the aircraft with the known inaccuracy and that safety was not compromised. Unfortunately pilot training at its basic level rarely includes this kind of detailed training - not because the aircraft maintainer/operator can't give it, but because the pilot trainee is unwilling to pay for the extra few hours of training it would take to be presented with such worthwhile training. PPL students, please consider this while you're whining about the cost of flying instruction. There are many things that are not even mentioned during PPL training, which a pilot really should understand, before they start making these types of go - no go flying decisions. Unfortunately secondary indicators of this type rarely come with the accuracy requirements, and calibration records which things like airspeed and altimeter do, so airworthiness decisions about these intruments can be less clear. If the letter of the law has been met, the pilot must then decide if the spirit has been met - is safety compromised?
As for a "minimum equipment list" it is extrememly rare for a "light" aircraft to have one at all. If there is one, it is formally approved, documented, and readily available to the pilot. Generally the requirement for minimum equipment for such aircraft is found in regulation, such as the one I cited earlier. Those regulations do convey some "give" for allowing operation with U/S equipment, though, for what I see, a record of this is still required. For obvious reasons, a "pilot" with no other appropriate qualification, is not authorized to go beyond the combination of the regulation, and the infomation conveyed in the aircraft flight manual. If in doubt, the pilot must seek further information from the appropriate maintenance facility. Certainly, this can be handled verbally at first, with the possibility that the maintainer might explain to the pilot why the observation can be considered as not requiring a documentation of a snag, for any of a number of reasons. This is a part of that pilot's training.
Now, it appears that my phrase "..with a known defect..." dd not clearly convey my meaning in this context. The Concord's operation and maintenance environment is well outside the scope of the normal GA pilot, and the aircraft sitting on the ramp. Yes, years ago, I was sent to New Zealand to evaluate for purchase a DC-8-50, which had a known defect (6" long crack) in a main landing gear forging, which was being operated "on condition" with all of the appropriate engineering and inspection oversight. That's not what I think that we are talking about here...
Nearly all aircraft have Structural Repair Manuals (SRM's) approved as a part of their design (and I'm confident that an interested pilot would be permitted to leaf through one upon request - they're not a secret or anything). These manuals describe repairs for damage and wear and tear type situations, which the aircraft manuafacturer knows by experience could be required. There are certainly many which come to light during a service life, which the manufacturer had never envisioned, and thus are not described. For GA aircraft, it is not common for SRM's to be reissued along the life of an aircraft to include additional information, though Service Bulletins are issued to cover this situation from time to time.
It is an unfortunate oversight in our aircraft documentation system that there is generally no formal way to actually indicate on the structure of an aircraft itself that a defect (crack) has been detected, inspected, and is being "watched" within the scope of an approved means. So, in fairness to the pilot, a "minor structural crack" could be prefectly fine, but the pilot has no way of knowing this. there will most likely be a reference to this in the maintenance records for the aircraft, but a review of these records to that wlevel of detain, by the pilot, prior to a flight is beyond anyone's expectations.
So, if in doubt, ask, and document. At worst, the maintainer of the aircraft will realize that the frequent written reports of a know defect warrant a note in that area which says "yeah, we know about this, and we're watching it - thanks for noticing!). If still in doubt, don't fly the aircraft!
don't have a clue about what engineers can and can't run with
In fairness to pilots, many aircraft maintenance personel, and design type engineers, also have no clue about what they "can run with", if they're not familiar with that aircraft type - but they should know where to enquire to get the right information, and be able to apply it!
Pilots who take the time to learn as they go, when they encounter such situations, make our industry more effective, and look better to the public.