The mumps vaccine is certainly not one of the most effective ones. However just having the majority of mumps cases be in vaccinated people does not mean that the vaccine is ineffective - in a highly vaccinated population, and while the vaccine is still protecting many, there can be more people walking around having been vaccinate with a mumps vaccine that failed/didn't take than there are people who are actually not vaccinated. That the disease is still limited to outbreaks and has not returned to being a common childhood disease that nearly everyone gets at some point is due to herd immunity.
Pertussis is a problem. I've heard it suggested that the newer vaccine may not be as effective and that we've bought a modicum of vaccine safety with the far more terrible price of letting a deadly disease return, that we would have been better off sticking with the old whole cell vaccine. Or I've heard, as suggested in this article, that the bacteria has mutated (as bacteria is wont to do) and the vaccine is not as effective against the new strain. In either case, the vaccine did serve its purpose and made pertussis a very rare disease for decades, but it may be time for a new one.
On the other hand, the measles portion of the MMR is a very effective vaccine. Measles is very rare in vaccinated people. While it can happen on occasion that a few vaccinated people will get it in an outbreak, the vast majority of measles cases occur in the unvaxed.
I always wondered about the herd immunity thing because when talking about the MMR vaccine, if the vaccine is not 100% effective, and it does in fact shed, even if everyone in the world was vaccinated against measles, it can still be spread between the vaccinated population. Shedding from newly vaccinated people and thus infecting others where there is vaccine failure (not 100% effective) So, is there ever a such thing as herd immunity in that case? Also, it doesn't confer life-long immunity either, so unless everyone continues getting vaccinated for it throughout their entire lifetime (certainly not promoting that), there will never be a said herd immunity. I could be totally off base but that's how I see it. Sometimes I wonder if we are keeping the virus contained in the country by the vaccination. As long as we continue vaccinating with MMR, the measles virus (vaccine virus) will always be within our community and will continue to circulate and resurface.
As I wrote above, measles is very rare in fully vaccinated people, the vast majority of measles cases are in people who have not even had a single measles vaccine. Shedding is a real problem with oral polio vaccine, chickenpox vaccine, and the inhaled flu vaccine. While the measles vaccine could theoretically shed and cause measles in someone else, there is not a single documented case of it happening, so if it does ever happen, it is an extremely rare thing. Also, while only time will tell for sure, it is currently generally believe that the measles vaccine does induce lifelong immunity.
Measles has pretty much been eradicated in the US, only it keeps being brought back from overseas. It is the vaccine that keeps these imported outbreaks relatively small - stop vaccinating for a 5-10 years to let a large population of completely unprotected little kids build up, and the next imported case that infected one of them wouldn't be limited to a handful of cases or even a couple hundred, it would spread like wildfire and cross the entire nation.
It would, in theory, be possible to eradicate measles entirely, it is only political situations and poverty and such that has kept large populations from being vaccinated in some areas and thus allowed measles to thrive there and continue to exist.