Today I put up mezuzos for a local balebos who built a new house. Besides for buying beautiful mehudar mezuzos, the owners, who intend on living in the house for many years, instructed their builder to chisel out a compartment in the door frame for the mezuzos to fit into. Then, for extra protection, a perspex panel was screwed onto the wall to cover the mezuzah (see picture).
This concept is not very common today, but it used to be common in times goneby. Perhaps it's time to reintroduce this concept, for the following reasons:
1) It is undoubtedly halachically superior to many other ways of affixing a mezuzah. Many of the mezuzah cases available today are made of two pieces, with the mezuzah sitting in the front part of the mezuzah case that is often not even connected to the wall in a permanent manner. This is because when affixing with glue or double sided tape only the back part is properly affixed to the wall. Even if you tape the front part to the back, something a lot of perople do,( or even tape the mezuzah to the back part of the mezuzah case), is standard scotch / sticky tape really considered kavuah? Most poskim say no.
2) It actually looks very nice and classy, plus you can see the mezuzah which is a hiddur.
3) It is easy to take down and put up when checking - much easier than nails in which one can end up scratching paint and making multiple holes in the walls (from every time they go down and up). And it is certainly less messy than mounting tape or glue.
The obvious disadvantage is that you make holes in your walls which may not be appreciated (or allowed) when renting a house from a landlord. However if you own the house and plan on living in the house long term, I should think this is definitely a great way of affixing mezuzos.