As with anything created by a human, a clerical error is always possible, but since in many cases dates such as these were related to pay and allowances a soldier might receive, extra care was taken to ensure accuracy.
It's worth explaining how information came to be recorded on service records. The master document was maintained in a Record Office in the UK, usually in a location well away from the units it served. In the main part of the records you will see a column on the left hand side headed Authority or similar. This is where the source of the information is recorded. If a soldier was posted as an individual the authority was likely to be a posting order initiated by the Record Office. If it was a unit move, the authority will probably be a War Office reference. For example, in your first photo, the reference DO stands for Draft Order, ie a unit move. If the occurrence was something that happened within the man's unit, such as a promotion, leave, going into hospital, attending a course etc, then the unit would send this information using what is known as a Part 2 Order. These were typed out in a predetermined format by a clerk in the unit orderly room and sent to the Record Office. Usually this document, containing information about several soldiers, would be compiled on a weekly basis, and would have been sent by post, so it could take some time to arrive back at the Record Office. All Pt 2 Orders were serial-numbered so if one went astray the Record Office would know and could ask for it to be sent again. A Part 2 Order would give a start date for whatever event was being notified, and might give an end date in the same order, or in a subsequent Pt2 Order. Therefore the Record Office had a complete duplicate of whatever was recorded in the soldier's unit about him.
There are parts of a soldier's record which are not maintained in this way. One example is your third image which relates to the soldier's medical history. This will be a combination of opinion by a doctor or medical orderly, eg a diagnosis, or facts, such as when he went into hospital (the hospital would also use a specific form to notify the Record Office, similar to apart 2 order). And lastly a medical entry might be based on what the soldier himself answered, as you can see in your example where it says "in what countries have you served and for what periods?" Clearly there what has been recorded is based on the soldier's memory after the event so may be inaccurate.
Other parts of the record may also be based on what the soldier said, for example in earlier, pre 1930s, enlistments the soldier would give his age in years and months but since he wouldn't have been asked for his birth certificate, it was easy for this information to be wrong. This doesn't apply in your case as, by the 1930s, enlistees did have to provide a birth certificate.
The overall rule is that throughout his career a soldier had to 'belong' somewhere. The chain of Part 2 orders and posting orders etc should have no gaps. A soldier would be struck off strength of his first unit and taken on strength of his second unit on two successive days. Obviously if he had to travel, perhaps by sea, he could not physically move between units in a single 24 hour period. Therefore the date he was taken on the strength of his new unit would often indicate that that was when he started his journey. Before long transits by sea it was usual for a soldier to be given embarkation leave, perhaps as much as 14 days, in which to see family and to gather any additional necessaries for his overseas posting. Similarly a soldier returning from a long posting overseas might also get disembarkation leave. At times a soldier might be posted to something called the Y list. This was a paper exercise to account for things like long term sickness, long courses away from the unit and so on.
Leave was always possible during peacetime, but if a man was serving in Palestine in the 1930s it is highly unlikely that he would have been able to get back to the UK, due to the time it took to sail from the Middle East to the UK, and back again. The exception might be compassionate leave, perhaps because a parent was dangerously ill or dying. In a case like that, due to the urgency, a soldier would probably be moved back to the UK on an RAF flight, and to return to his unit the same way. If a civil airline was available that too might have been used (and paid for by the Army) instead of the RAF. A soldier is unlikely to have been able to pay for civil air flight for ordinary leave.
