This depends on whether you are talking about labor disputes within the context of a collective bargaining agreement or outside of that context.
If a workplace already has a collective bargaining agreement, the major source of labor disputes is allegations from union members that management is not following the rules laid out in the agreement. There will be disputes over whether disciplinary procedures are being followed or whether supervisors are trying to force workers to do things that are not in their job description. The contractual means used for resolving such disputes is typically a grievance procedure. The contract stipulates how grievances are to be filed and who is to make the final decision.
If you are asking about disputes prior to collective bargaining, the major source of disputes is labor's desire for higher wages, better conditions, and more job security one the one hand and management's desire for lower costs and greater flexibility on the other hand. These disputes can only be settled through collective bargaining and compromise. If collective bargaining does not work, one side or the other can impose a work stoppage (the union strikes or the firm locks the workers out) to try to force the other side to come to a contractual agreement.
This is a great question but it is rather broad. There are many reasons why there are disputes. Therefore, it is not possible to name all the reasons for the disputes. For example, some unions may want more money or better bonuses or better hours or more benefits. As you can see the issues are various. In the end, the certain thing is that there are conflicts because groups are not happy with the status quo. They want change.
In terms of means of resolving them, there are are few ways this can be done. The easiest way to resolve anything is when both parties agree on some compromise. In other words, both sides see each other's points and they come up with a resolution that both sides can agree on.
If this does not work, then the union has other avenues, because they can strike. If they take this route, they can cripple the company that they work for, because nothing will get done. Productions comes to a halt. We call this collective bargaining, because the union speaks in one voice for the sake of many. When this happens the union has a much greater voice.
In the past, America was really a land of unions. However, in more recent times, unions have gotten much weaker.