For me personally, these have been sticky points (and I was Montessori-schooled as well):
*Parent community. Because Montessori often discourages parents in the classroom - and I completely understand the philosophy - parents would still like a way to be involved in the school, not just annually at the auction or whatever fundraiser is going on. We want to meet each other, help make materials, and truly create a learning community, etc etc.
*Explaining Montessori teachings at a laymans terms. A lot of the terminology is somewhat obscure to parents (i.e. "normalized") and needs to be translated. I do understand, but most I would say at my daughter's ex-school do not. The writing and reading philosophy for example, is very in tune with modern child-led learning (i.e. writing before reading, reading based on phonemic awareness), but is still explained in terminology that can be very frustrating to hear due to the somewhat old-fashioned nature.
*Emphasizing the social skills that children are gaining in the classroom. Sometimes the teacher or method can come off as very brusque, or individualism to the exclusion of social awareness and responsibility. It shouldn't seem like the Ayn Rand Preschool of Hard Knocks, because that's not what was intended - i.e. the way older children are encouraged to help younger, etc. But many parents get this impression in any case.
*Being flexible with the stages and progression. I do not think that children always progress through them the way as is taught in AMI/AMS training. Some kids (i.e. mine) will skip around. She read before she wrote. She likes fractions before adding four numbers. She hates almost all the sensory work, the red rods. She loves learning about space, even though this is typically not worked with until elementary stage. A little more following the lead, a little less trying to figure out where the child fits into the binder's prescription of the stages.
There are probably other things too, these are my issues that I think could be addressed and would make a Montessori school great.