The front on the northeastern part of the empire was so huge that the difficulty in maintaining it, and Rome must have spent considerable time and resources in defending itself against invading barbarians.  In retrospect, was there anything that Rome could have done better to defend itself so that its defense was more efficient or more effective? 

Yes, use diplomacy and share their technology with them.  Eventually they would have been able to have commerce with the barbarians, or at the very least divided them enough to where they couldn't threaten the empire itself.

But don't you think the barbarians were already divided quite a bit as it was?  We know that the Romans and barbarians engaged in some trade as it was – for example, with the Visigoths.  Are you suggesting something on a larger scale that would them to be more reliant on a stable Roman economy?

I'm not sure anything would have worked beyond brute force, but the Romans galvanized the barbarian hatred for them with each expansion campaign.  It was not the barbarians that did in Rome, it was Rome who did it to itself.  But your question is valid, especially since once the barbarians broke through and conquered Rome, the transition didn't seem to be that drastic (well to me anyway).

DEFENSE IN DEPTH.  This is a strategy Rome did not try until it was too late for them to make it work.  They violated one of the first rules of warfare with their border, they tried to defend everything.  The old maxim that “he who defends everything, defends nothing” is true.  The Limes were doomed to failure as soon as the decision to build them was made.

“Limes” is the Latin word for frontier or border and also what historians call the series of fortification they constructed along that frontier to keep the barbarians out.  The Roman Limes in Europe   In many places the Limes were actually earthen walls with periodic forts and patrolled by the local garrisons.  The Romans attempted a linear defense of a border that was almost 2,000 miles long with an inadequate force.  At it's height the Roman Army could put in the neighborhood of 200,000 troops in the field, maybe double that if you include local informal militias.  Simple math will tell you that is about 200 men per mile, not even close to enough troops to seal the border even if they could have put them all in the north, which they could not.  What the Romans needed was a defense in depth, they failed militarily and eventually invited the barbarians in to help defend against other barbarians, that was their ultimate failure because the Barbarians in the Empire were only loyal to a point and not unconditionally as native Romans were.

Ah, but if the Romans had opted for a defense in depth from the get-go they may have been able to get by for far longer without resorting to barbarian auxiliaries in the first place.  Unfortunately, the demographic trend was against them and their birth rate declined as their wealth increased; something that has been true of successful cultures throughout history.

Do you have any particular circumstances in mind?  Or just a general feeling that population decline was out of their control?

I was referring to diseases that likely hit.  Here are some circumstances from “The Early Middle Ages” (Philip Daileader): “1. Archaeology has revealed a gradual decay in Roman towns and cities from perhaps as early as 200 A.D.  Century after century, the inhabited area in most Roman town and cities grew smaller and smaller. …  B. The origins of depopulation are still somewhat mysterious.  Climatic changes and the barbarian invasions probably played a role.  However, the most important factor would appear to be epidemiological, given that new diseases entered the Roman disease pool from the 2nd century onward.”

So why didn't these diseases affect the barbarian hordes as well?