The wiki article has a lot of flaws. Dušan never captured Adrianople; in fact, there was no 1355 campaign against the Byzantines. At the time, he was busy with affairs in the west, and some of his most trusted generals were engaged there. Also, Bulgaria was a junior partner - but not a vassal - of the Serbian Empire. Neither was Bosnia. There was no major persecution against Catholics, the Pope didn't run a conspiracy against Dušan, and so on.
However, this is still a very interesting idea. Capturing Constantinople was known to be one of Dušan's biggest ambitions, and it was definitely possible at certain times.
So, let's say Stefan Dušan launches a successful campaign against the Byzantine faction of Kanktakouzenos and takes Constantinople around 1354-55. What does this mean?
-It's important to note that Dušan's conquest of the Byzantine Empire wouldn't be a total foreign takeover. Dušan was technically allied to one of the Byzantine factions (the faction of John V Palaiologos), and there were even some Byzantines who wanted to invite Dušan into Constantinople and make him their Emperor.
So what probably happens is that Dušan proclaims himself Emperor in Constantinople, merging the Serbian and Byzantine Empires...but John V Palaiologos also keeps his title (for the time being, anyway). John is forced to acknowledge Dušan as his equal and co-ruler of Byzantium. Well, they'd be equal in theory - in practice, Dušan would be the one calling all the shots, and John would be a fancy regional governor. Or a totally helpless puppet.
In time, the Palaiologos dynasty might be deposed, leaving the Nemanjić as the only ruling dynasty of the Serbian-Byzantine Empire. Or the two dynasties might peacefully merge into one.
-The Serbian-Byzantine Empire will not break-up like in OTL. This break-up was linked to some highly specific circumstances - circumstances which probably won't be repeated here. Also, the prestige of the Nemanjić dynasty would be through the roof after capturing of Constantinople; the Byzantine state machinery will open up new possibilities for centralization; and the troublesome magnates will be too busy digesting new honors, offices and duties to screw anything up (much).
-The Ottomans are no joke, but in this particular scenario they don't stand a chance. Dušan would be able to attack them with the might of the entire Serbian Empire and the resources of the re-unified Byzantines and call in Bulgaria as an ally, if needed. Total overkill. The Ottomans will be thrown back across the straits. Gallipoli will be rebuilt and fortified, possibly with a permanent garrison of German knights.
However, I don't think the Serbian-Byzantine Empire would cross into Anatolia. Those lands are lost to the Turkish beyliks - maybe for some time, maybe forever.
-It's springtime for Venice, and not a great time for Genoa. The Serbian Empire and Venice were very friendly and Dušan's takeover of Byzantium means Genoa's privileges and influence are largely replaced by Venice's. Dušan even promised to transfer some towns in Epirus to Venice if they help him take Constantinople. Venice's rise could present a problem in the long run, but in the short run it's nothing to worry about.