People have mentioned it before in a general sense, but not specifically, is how multi-classing will affect his Ability Score Increase / Feats. In 5E that is handled strictly at a specific level of a specific class, not per total character level.
The first one of those is always given at 4th level for every character. So, (rhetorical example that will never happen) if someone only took 3 levels of each class, and took 7 different classes, they would never get one.
By taking Rogue 3 / something else, he will get his first ASI/Feat at 7th level. At 8th level, every other class except the fighter gets their second; the pure fighter gets their third.
So, if you're on point buy, the extra breadth gained from the multi classing will be additionally balanced by the lower skill ranks, spell DCs, saving throws, etc. from their ability scores not moving up. Or, it will limit some options of customization by Feats.
Even given that, I have to slightly disagree with some others; I think 5E multiclassing is the most balanced of any edition I've ever used. It's not completely written off as terrible, it's not automatically adopted by every min-maxing twink; it makes for hard choices, because you get so much - by giving up so much. It's really hard to fall into a sub-optimal 'trap' choice compared to other editions.