The classics: sleeves that are too long and cover the shirt, a chest that is too tight and creates X creases at the buttons, a collar that lifts off the neck, a jacket that is too short and ends at the widest point of the hips. Add trousers with the wrong length that break in several places, or, conversely, are too short and look accidental. Each of these on its own may seem like a small thing, but together they take away the result you are paying for.
Tailoring alterations are your ally, as long as you are not trying to fix a bad base. Shortening sleeves, taking in the waist slightly, adjusting the trouser leg, correcting the trouser waist, these are realistic and sensible actions. Changing shoulder width, a major chest rebuild, or altering jacket balance is a different league. That is why I put such emphasis on shoulders and chest at the start of the fitting. It saves money and disappointment.
In practice, it is also worth thinking of a suit as a set for specific situations. You will choose a different level of fit for an all day job where you sit, stand, and talk, than for an occasion where you mostly stand and look good in photos. If the suit needs to be “for everything”, choose a compromise: moderate fit, wool in an all season weight, and classic proportions. A good suit is an investment that should serve you, not force you into constant adjustments.
Finally, a small but important point: shoes and accessories also affect proportions. A slimmer shoe visually lengthens the leg, a chunkier one can shorten it. If you want to organize the topic, take a look at: Men’s shoes: how to choose a pair for a suit?. And if you are looking for a classic pair for many looks, as an example I can point to Buty Loafer Nero, which pairs well with elegant trousers and summer sets, as long as you keep the trouser length in check.