One reason for disputes during the probate process is that one sibling gets selected as the executor for the estate, but then the other siblings feel like their actions during the process are not fair or not in keeping with their parent's wishes. In some cases, they may even feel that the executor is acting illegally to benefit themselves.
Whether or not that is really happening -- the other siblings could be mistaken -- it can cause a dispute and even a will contest. One key step to take to prevent this outcome is for the parent to select a third-party executor.
Parents often pick their children because it seems easiest to them or because they assume the child will understand their wishes. However, it may be better to have someone who has absolutely nothing to gain. That removes any questions about their motives.
This is especially true if the will is going to leave unequal bequests to the heirs. The parent may have an excellent reason to do so, such as feeling that one heir needs more financial assistance than the others. However, if the heir that receives more is also the executor, it can raise questions. When a third party announces the decision, the heirs are more likely to go along with it and assume it really is what their parents wanted, even if it is not what they would have preferred.
As you can see, there are many ways for estate disputes to arise during probate, and these cases often get very complicated. Make sure you know all of your legal options.