As far as I know a muslim is expected to follow such rules as the direction to face when praying and the time of prayer etc to the best of his / her ability. If they do not know the correct direction or time (as may happen for example in situations here on earth, for example in a prison cell, then they just do the best they can. The same applies to many other things such as hallal food. They are expected to do thier best to ensure that what they eat is hallal but if they mistakenly eat food that is not hallal then it is not such a big problem unless it is thier fault eg if they are decieved.
They do already have problems with the exact time and date to celebrate cirtain dates (such as eid) around the world due to time zone differences etc and this can cause divisions in society if two groups disagree on the proper time/date. However they are much less fragmented than the Christian religion. In my home town of livingstone, Zambia, population approx 100,000. there are about 150 different Christian denominations.