According to this homepage (link is in Japanese only), there’s more to a delicious mikan than just sweetness. It’s the balance between citric acid and sweetness.
Apparently, you want an orange with a sweetness factor of around 10 and a citrus acid level of 1.2. So how can you tell which oranges are going to have the right balance of sweetness and citrus?
Size: The big ones always cost more so they must taste better, right? Well, actually the small ones are sweeter, so go for the “M” or “S” size.
Shape: There are some varieties of mikans that are meant to be round, but in general, flattish ones are better. It’s also good to look at the bottom because is should be slightly indented. Among the fast-ripening varieties the ones that should be more roundish are called wasei unshuu (Japanese: 早生温州) and the ones that should be flat are called gokuwasei unshuu (Japanese: 極早生温州).
Color: You can sometimes find greenish mikans early in the season that are sweet, but in general, the darker the orange, the sweeter it is. Apparently, mikans early in the season sometimes have orange coloring added (link is in Japanese only), so they are going to be sour. Most places stop adding coloring to mikans that are produced after the beginning of November, but there are some that do it throughout the season, so coloring isn’t the best way to choose an orange.
They say you can tell that a mikan has been colored by looking at the stem. If the stem is really yellowish near the fruit and brown at the top, it’s probably had coloring added.
Hardness: Juicy mikans are not necessarily sweet, so choosing one with a loose skin or that is very soft doesn’t mean you’re going to get a sweet one. Usually the juicy ones are less flavorful. Touch the skin, and it should be a bit soft, but with resilience. Ones with hard skin are usually not ripe yet.
Stem: Surprisingly, all the homepages I checked emphasized that examining the stem is an most important step in ensuring you’re going to get a tasty orange. Thin stems are better because they come from thin branches, which apparently makes them sweeter. Also, check the stem’s color. Mikans’ stems turn from green to yellow as they ripen, so a yellowish stem means the orange will be more flavorful. Darker stems mean less taste.