If you don't have a problem with water pooling any more, the real answer is probably to have a professional roofer look closely at the roof both on the inside and outside. The problem with a lot of roof leaks is that where the water shows up in the house isn't where it comes in. Water has an annoying tendency to run along internal beams and such, then come into the house far away. You can go over any edges with new tar and hope you catch it but in my experience this approach ends up being like playing whack-a-mole, you patch and wait for it to rain, then patch more and wait more, etc.
So I would say if you can do it yourself, look closely at the underside of the roof as well as the outside. If you don't find anything, a professional roofer is probably in order.
Any moisture issues related to the standing water incident would have manifested itself long before now. Whatever the current issue is, it's unrelated to the previous issue. In that time, it is possible a new leak developed. It's also possible the dark areas are related to interior humidity and unrelated to the roof. In cold weather, the ceiling surface under rafters is measurably cooler than the nearby portion under insulation alone. This can cause condensation only under the rafters. As you know, condensation can lead to mold.
Can you tell if the darkening is due to actual mold? The damp surface can attract dirt that darkens the area even though no mold is growing. Even though the dirt can stain, attempting to clean an area with plain soap and water would yield a very different result than if mold is actively growing.
If mold is actively growing, it is time to consult with a mold professional. They will determine the cause, mitigate the mold, and suggest how to prevent it from happening again. If you want to investigate further before going that route, the only reliable way to determine if the rafters are getting wet is direct inspection.
Cut a small inspection hole where you think it's the worst. If it's wet up there, a lot more ceiling is coming off, so don't bother patching the hole. The roof is leaking. It needs to be repaired and all wet drywall and insulation needs to be replaced. If it's all dry, breathe a sigh of relief. The need to patch the hole is much less than it could have been. Be sure to adequately seal the damaged vapor barrier.
If the rafters are dry, the only thing you can do to reduce condensation on the ceiling is reduce the overall humidity of the house. First try selective ventilation and lifestyle adjustments. Consider bumping the thermostat up a bit. If that's not enough, look into continuous ventilation through an air to air heat exchanger.
A far as replacing stringers, that cannot be done with comp roofing unless a full cold roof is installed. It is normal practice for concealed structural spaces filled with insulation to not be ventilated. It sounds like the roofers followed conventional building practice.
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In the end, the roofing company had ceased to exist which was why it was difficult to get hold of them.
I got a reputable building company to sort out the cracks in the walls and weatherproof the render - they did an amazing job and they even found a fault in the way the new roof was fitted... and fixed it for free. The fault was that the new roof was just a new covering (although well fitted and looked good to the untrained eye), but it required some lead flashing (like a skirt) to force water run-off from the walls to run onto the roof and towards the drain/drainpipe. Without the flashing the water was allowed to run between the roof covering and the wall itself, hence leaking underneath in particularly wet weather. The issue never returned.