Most people have had good experience with Fluke for warranty service, that is from the most of the reports here. This has been one of the big selling points for Fluke is that they have a great warranty and take care of people. You seem to be having more problems than most.
Perhaps they have better service outside of the STATES... 
Yeah sure, good luck. Try to order a Fluke spare part. The Dutch department does not even respons most of the times. The only one helpful up to now is Fluke USA.
About quality. I have a Fluke 720 KV divider. It was not used for over 20 years and stored in a climate controlled room. (at that time the callab was turned into a computer server room but all cal gear stayed there unused until it came to me a few years ago)
http://www.pa4tim.nl/?p=2332 lots of cracked plastic, tried to order parts over here but never got a response.
A Fluke 8020, together with a Norma DMM stored in the half open barn from a friend for over 25 years. The 8020 needed a new display because it became black (probably due to low temperature), I replaced it and it still works great and is still spot on. The Norma had a fungussed leather case but the meter itself worked after I renewed some solder joints. That meter does not use screws. Every part is clicked together and to my surprise all clips are stil intact and not became brittle.
I have a 77-III, found it in the mud about 20 years ago. Used it in my garage over 10 years. The yellow was complete black from oil, about 10 years ago I moved it to my lab, cleaned it and use it still without problems. No screw problems.
My >500 dollar Agilent is only used in my lab. The plastic foam of the probes falls apart, the outside of the meter also, had to replace the common bus because it broke inside the plastic. But it is still spot on and I use it every day for my job (repairing test and calibration gear in a clean lab, never used it automotive)
About plastic softner problems like in the Agilent. The steering wheel of both my old LandRovers became extreme sticky. The body of one of my Nikons idem. Almost all old HP instruments I have or have seen, have a sticky surface if it was "rubberized" (I do not know what they put on there)
I have several old Tektronix plugins for the 500 and 7000 scopes. I the 500 all vernier potmeter connections are split in almost every plugin. On the 7000 knobs break and other plastics to. They were pretty expensive in those days.
I have seen several Flukes with function switch problems where cleaning the black stuff or other tricks did not work. I have seen several broken display clips in 80 series. Several Fluke scopemeters with display problems caused by glass bonding coming loose (also in several G&M secutests, it is often fixable but I do not know for how long). But no bad experience with the screws in Flukes. Funny however that all dead Flukes I have seen that were killed in action had the safety parts still intact. One 123 scopemeter had a dead display and two dead ASICs. It was working fine until it was stored over night in a car while it was far below zero.
But we are talking about gear that is over 20 years old. It is not build for eternity but comes close

Most gear from that age needs some TLC now and then. I have a collection analog meters and those are even older but some have also cracked cases, worn screwholes, broken plastic etc. I do not know the history of most so no clue what caused the problems. After so many years things can go bad. I have owned cheaper meters over the years but not one survived. If you look at the price per year the Fluke is not so expensive. And most important they stay in cal and can be trust for the primary use: measuring