The three materials used in monolithic domes are not the most environmentally products available. Vinyl and polyurethane are both petroleum-based and the latter emits toxins when it is burned. Shotcrete is lasting but has a large initial CO2 footprint.
The airform is a delicate membrane which can easily become damaged by falling trees and vandalism. Once it is damaged, water could seep into the underlying insulation and become a big matted sponge. Steps could be taken to protect the airform with aluminum, but this can be expensive.
The monolithic dome creates a tight hermetic seal, which is not always desirable given that activities like showering and cooking require dehumidification and forced air ventilation. To rectify this issue, a hole can be created in the center of the dome to circulate air.
Building a monolithic dome may require special permits depending on the type of structure you have in mind. A monolithic dome for a greenhouse may not need a permit, but if you are building one for a residence or larger structure, check your city's ordinances for construction of such domes.
Furthermore, monolithic domes are not everyone's cup of tea. A home that is a monolithic dome may not fetch the highest price, given the idiosyncratic style. But as an addition to a conventional home, such as a pool enclosure or sheds, a monolithic dome could add to your property value.
Adding additional features to your monolithic dome could be challenging, as traditional rectangular doors and windows cannot conform to the shape of a monolithic dome (unless the dome is built on riser walls, in which case the doors and windows can be placed there). Round windows could circumvent this problem.