The disputes will be attended to by the operator of the Mostro where the dispute is opened (the idea is that there are many mostros and the orders can be seen in one place so that liquidity is not diluted) then when the operator of the mostro (or the solvers who designate) takes a dispute will contact those involved and explain the procedure. 

By aspiring to be decentralized with many Mostros there will not be a single way for the Mostros to resolve their disputes, each one will be able to use the resources they see fit.  

But in the operational Mostro until now there have been no disputes (few users still use it, the quantities are limited up to 20k sats and they are generally users who act in good faith doing tests) but the way to resolve them is quite similar to Bisq each user must Provide proof of payment or receipt before a certain time and the solver will determine who is right

If you have a specific proposal you can open an issue at: https://github.com/MostroP2P/mostro