Who/what determines the order of articles appearing in an issue of an academic journal?

It is the editor, that determines the order. Other than that there are no general rules. Typically, they just pick the order that "makes sense". Maybe a topical article first if one is available. Maybe there are a couple of articles that fit nicely together, and (s)he wants to emphasize that, etc. etc.

Some common "clever" ways:

• By topics: The journal covers several topics and their order is preserved throughout the time.

• Highights/special issue first: Sometimes a part of the issue is a special issue for some conference or such; this would go first. Also, if you have a particularly notable article, it could go first, too, also articles to which the issue cover relates could go first.

• By whatever the editor deems related: I mean, the editor can do whatever he wishes, so whatever he considers relevant.

Some common "simple" ways:

• By order of acceptance: This allows final page numbers to be assigned once the final version of the article is available.

• Alphabetically by first authors: The simplest of all, in a sense.

Note that I don't necessarily consider "clever" better than "simple".

What a particular journal does varies, there are different motivations. For journals that people do not get in print much, there is a prevalence of the "simple" ways as the order does not really matter. For those that are read in print (think Science, Nature or even less strictly scientific titles such as National Geographic), some "clever" ways are usually chosen and more fine-tuning is usually done in order to provide smooth and comfortable reading.