Just as an idea for a Roman Empire that dominated the known world:
As far as I can tell, it came down to a few major points in history. Much as we call Augustus the mightiest and first Emperor, he also was the emperor that Rome began its decline in.
Simply not true: Rome's decline did not begin until after the period of the "Good Emperors", and even then, it still took two centuries and strong external and internal pressure for the
western Roman Empire to collapse. There's also the other side of this argument: it is thanks to Augustus that the Republic's decline was halted (even if it was just replaced by the principate, the principate was better in general): if not for Augustus, civil wars would have continued to ravage the Empire and it would have declined far more quickly and wouldn't have achieved the absolute hegemony it did IOTL.
Now, there were three or four key flaws in Augustus' reign:
1. Augustus attempted throughout his reign to promote ideals that were considered old-fashioned, but he failed miserably.
He did not fail miserably; he "imposed" certain conservative laws and was then rather lax in their application, because as carlton said, these reforms were more a way to placate the conservatives and traditionalists than it was any genuine attempt to turn back the clock socially.
2. Marriage to his wife Livia was, as far as I can tell, one of his worst mistakes. She married him perhaps with a bit of love, but she most likely married him to further her son's future and to advance her own.
She married the emperor: even if there was love involved, you can bet that foremost in her mind was the advancement of her son's career. All the same, she is not the main person responsible for the disastrous emperors that would follow (and neither was Augustus for that matter, but that will be covered in response to point 4)
3. Augustus selected Quintilius Varus to defeat the German tribes-- this was his worst failure. If he had selected a better general, his conquests might have been pushed farther into barbarian Europe.
Again, as carlton said, Varus was not actually a military appointment but an adminstrative one. Furthermore, the disaster at the Teutoberg forest was just as much a result of good planning and merciless execution on the part of the germanic tribes than it was naivety on Varus' part.
Keep in mind also that there was little chance for further expansion beyond Germania: not only was there no political will to push even further into barbarian territory, keep in mind that there were far more pressing matters militarily than pushing the border further north, chiefly, the constant Parthian threat in the east.
4. This could tie into 1 and 2-- Augustus was unable to find a political heir suitable to the task of defending Rome and maybe pushing it further. Rome might have survived longer if Tiberius was not in charge.
Nonetheless, Augustus still did a fine job of ruling Rome, but I believe these factors tied into Rome's fall.
This is simply not true at all: Augustus had infact found a suitable heir, two actually, his grandsons by Agrippa. If contemporary accounts can be trusted (and truth be told, they can't really considering all contemporary accounts are from his personal historians essentially), either one (whose names escape me right now...) would have been more than capable successors, and would have secured the Julian dynasty. Sadly, they
both predeceased him, and so he was left with his eventual successor Tiberius and the resulting Julio-Claudian emperors.
Of course, again as carlton already pointed out, Tiberius has been vilified by historians but honestly speaking he was by no means a bad emperor, in fact before his retirement to Capri he was a very efficient and even austere emperor who avoided most of the excesses of his immediate successors. The problem with Tiberius is that he made a lot of enemies and when he left Rome he left the empire in the hands of incompetent and greedy cronies who abused their positions to enrich themselves and tarnished Tiberius' reputation as a result.
Caligula at first was a very promising Emperor, but he unfortunately went off the deep end 6 months in and became increasingly paranoid, which is what resulted in his assassination as the Roman elites feared another round of purges like the ones that occurred near the end of Tiberius' reign. Interesting anecdote: the oft-quoted proof of Caligula's madness, his desire to name his favorite horse consul, was basically slander propogated by the senatorial class he alienated: in truth, what happened was that Caligula, facing increasingly intransigent senators, decided to show them who the real power in the empire was and so threatened to name a horse consul, just to show them how much that office meant. He was killed for it.
And then there's Nero, the early empire's black sheep... he was a good emperor. I know it might be hard to believe, but he was neither stupid nor cruel, he was not paranoid or crazy, he was quite simply a good emperor who just so happened to have a taste for theatre. His rise to the throne was a bit... merciless (he murdered his half-brother Britannicus and tried to murder his mother once he was emperor), but he was an otherwise effective administrator, and he was no more at fault for the fire that ravaged Rome during his reign than the english monarchs were responsible for the great fire of London. Again, he was killed because he alienated the senatorial class.
So, to sum it up a bit more succintly: sorry, you're wrong on all accounts.