I think MSC is a historical anachronism, often useful for bureaucratic purposes, but mathematically indefensible. For one, it is built as a tree with some weak "for xyz see ..." connectors, while a better form would be some kind of poset of subareas. Also, the reason arXiv seems better is because 1) it was invented later and 2) it has only large areas. If arXiv has sub-areas, 15 years later it would be just as bad.
Some years ago I was distressed by how Wikipedia treated the subject as well and completley rewrote/restructured the Combinatorics article, which is still more or less in the way I have made it. Based on that, let me comment only on MSC 05 (Combinatorics). Here is what we have:
05B Designs and Configurations
05C Graph Theory
Now, 05A is a fine category as long as you don't try to look at its sub-cats. For example, 05A40 is "Umbral calculus". Quick, show of hands for those who think this sub-area is comparable with 05A05 which is "Permutations, words, matrices". But let's not go there - more trouble is coming up.
05B. This would be a coherent choice if this was "codes, block designs and sphere packing" or something like that. However, by looking at some sub-areas you quickly realize this category has no structure at all. Essentially, anything can be "configuration" in the opinion of the MSC authors. For example, 05B includes "Matroids" (large area) and "Polyominoes" (not an area at all, sort of similar to "unit cubes"), which are and should be viewed as distant parts of Geometric Combinatorics. It also includes "Matrices" (hello?) and "Difference sets" (huh?). The most beautifully titled category is 05B99 "None of the above, but in this section", and given that 05B has no common theme, anything goes, I guess...
05C. In contrast with 05B this is a very clear and coherent category. It is also very popular and on a permanent quest for independence (the suggestion being that it becomes 07 which for whatever historical reason is missing in MSC).
05D. Should Shouldn't this be "Extremal and Probabilistic Combinatorics"? So if a paper proves a new result in Ramsey theory using probabilistic method, is it 05D40 (Probabilistic methods) or 05D10 (Ramsey theory)? Anyway, this is a clear category which should be linked to 60C (Combinatorial probability), which itself needs to be renamed "Discrete Probability".
05E. This would a clear category if the areas were more connected. As it stands, 05E30 (Association schemes, strongly regular graphs) should really go into 05B. Similarly, 05E40 is an important sub-area and should really go into MSC 13, or perhaps replaced by a better named sub-cat (every part of Algebra now has "combinatorial aspects" - should we list them all in 05E?), or even become a separate part of 05 (or of both 05 and 13, if MSC becomes a poset). Most strikingly, another important area 05E45 (Combinatorial aspects of simplicial complexes) should be taken outside of 05E (what exactly is algebraic about it?) and made into a separate part of 05 titles titled "Topological Combinatorics".
Ugh... In summary, this mess has to be largely redone. New parts of 05 need to be created (we have 21 letters F..Z remaining for "Geometric", "Topological", "Analytic", "Arithmetic", etc. - see Wikipedia page). What is left in each category would then be more coherent and searching for such cats in MathSciNet would actually make sense.