The doubts of independent groups, and the need for further experiments to confirm the results is the scientific method and community working as intended.
Ultimately, its mostly been the sensationalistic media coverage that makes the situation seem more controversial than it really is.
Struggling to come up with a simple example. Imagine you collect some data, analyse it and see a "3sigma" effect. You decide to collect more data to see if the effect keeps getting bigger or goes away. After collecting a lot more data you get "5sigma". This could be because it is real, or because you have an "unknown unknown"
If you had a systematic (as oppose to a random effect) shift in your analysis, collecting more data will make you more sure that there is an effect. Even though all you are seeing is the effect of the systematic shift.
For almost all analyses in particle physics (or astro or ...) we spend a huge part of our time evaluating "systematics", it isn't uncommon that this part of the analysis takes a lot longer than the nominal result. Unfortunately this only protects you against known unknowns. You can't take into account things you don't think of/check for.