Is there a problem with choosing to always follow the most lenient opinion in every Halachic dispute encountered? I'm talking about when the disputants are qualified poskim and the leniencies do not contradict each other.
The fundamental answer to this question is no. This has been brought up before and Chazal have stated that the principles by which particular rabbonim analyze situations and obtain a psak must be maintained
When a rav analyzes a case to give a psak, he uses the principles of halacha and it then leads to the psak. Thus, as an example, the principle can lead to a "kula" in one case and a "chumra" in another even though you do not see a contradiction.
Another point is that one may not realize when a psak is brought as a kula or a chumra. For example, Rav Soloveitchik gave a psak about melacha on shabbos. He is reported to have said "I am not maikil on shabbos, I am machmir on pikuach nefesh" (paraphrase from memory).
Thus one cannot go searching among different rabbonim to find the kulah as this is not how a psak is done. One must have a rav that one can ask sh'ailos and discuss what are the particular circumstances and stay with that rav.
The main concept is that if a rav is maikil in one case and machmir in another then there will be a contradiction if you try to follow his psak in one case and not the other.
As @DoubleAA said
Psak is an art of balancing the needs and details of the situation with the traditional legal arguments and principles. Picking things willy nilly based on what's easier is not Psak.
@Yaacov Deane points to