Interesting variations on a theme here...
The aircraft we operate, the Dornier 328 Jet (J328) has lots of little sensors hooked up to the EICAS (Engine Indicating and Crew Alerting System). Since this system is computer-controlled it can be a real-life example of The Law of Unintended Consequences.
The aircraft uses a single chime for an abnormality (yellow colour code in the CAS field). What can happen is that something pops up on the take-off run with a single chime and a CAS message, so that the PNF has to read and interpret the message.
There are some messages, such as 'Primary Anti-skid Fail', that could give real problems if you aborted, when you might end up with four flat tires. (The cleverly automated system sensed a failure in a speed sensor as you gathered speed on your take-off run, when it shut down the anti-skid system. Now it's up to you to select the standby brake system if you want skid protection, something not easy to do during an aborted take-off. The carbon brakes are very powerful, so that you could easily flat-spot the tires without trying very hard.)
And then there are other problems that might not pose an immediate safety risk but mean the aircraft will be grounded for maintenance after landing. You might as well knock it on the head then and there if you are at your home base, or else continue. It can take a minute to think just where you are once you think you know what is wrong.
And just to keep things interesting there are other alerts that usually mean nothing at all, being just false warnings generated by a speck of dirt on a sensor plate, perhaps. When you ask the Greenies what is up there they just shrug.
On top of all this we have the usual commercial pressure and also some pressure to avoid unnecessary passenger complaints. It is not an unreasonable amount of pressure, but there is enough of it to make the job of decision-making rather interesting.
Our in-house training staff have sifted through all of this to develop our SOPs. I often have a question about some point or other, often from stuff gleaned from sources such as PPrune, which can provoke some interesting reactions.