Under what conditions and circumstances might Rome have appointed dictators with practically unlimited governing powers?

The term Dictator did not the hold the same two bit Latin American sleaze ball connotation that we regard today.  I think in examining our forbearers it is important to keep a sense of perspective of who these people were and how different they were from us.
Until Lucius Cornelius Sulla Felix, the term Dictator marked a man of reverence and respect.  Think Father of Our Country style reverence.  They believe this because the Romans invested absolute power in one man to solve one problem for sixth month at a time.

The Romans hated the idea of Kingship.  They were jealous of their liberty.  They held their liberty in reverence and awe.  It marked his superiority against those people still subject to the whims of kings - read tyrant.

Athenian concepts of liberty and tyranny rested firmly in the breasts of the Romans.  The man who wielded dictatorial power only did it for a number of months.  From 509 to 83 BC, a period of 426 years, the Senate invoked the Roman office of dictator a mere 85 times and from the years 202 to 83 BC, the Senate had no need to convoke a dictator.

Famous men who held the office of dictator include men like Fabius Maximus, Lucius Papirius Cursor - twice consul during the Samnite Wars, Marcus Valerius Corvus, Marcus Furius Camillus five times Dictator and known as the Second Founder of Rome,  but the most famous dictator of them all was Cincinnatus.  Cincinnatus, who was living a type of political exile on his farm as his son had been convicted in absencia for political violence committed in defense of senatorial prerogative.  Messengers found Cincinnatus at his plow when called to service.  Cincinnatus mustered an Army and rescued the besieged Army personally by leading the infantry into battle and resigned from the office a mere 16 days in office.

By 202, the Senate replaced the office of Dictator with the Senatus consultum ultimum (the Final Act of the Senate) which empowered the Consuls with dictatorial power for a short window of time.
 

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What was the role of the proconsul as Rome expanded?

Prior to Hannibal, "a Consul had to become a General, because it was his business to look after the welfare of the State.  . . . [After Hannibal] a man became a Consul in order that he might be a General. The toga was made to give way to the sword, and the noise of the Forum to the trumpets."

- Anthony Trollope The Life of Cicero

A proconsul means a couple of things.  It means general and it also could mean governor.  The word in Latin means roughly "for the consul."  It meant that he who held such a title wielded power on behalf of the consul.  He acted with the highest trust of the state.

Prior to Hannibal, the resistance of the Etruscans, the neutralization of the Latins, the conquest of the Aequians, the Volscii, the dreaded Samnites, the resistance of Epirius and the first Punic War, few men held proconsular rank and held proconsular authority for any extended period of time.

After Hannibal, the Romans changed.  They stopped being a regional power and became a superpower.  A superpower being a nation that can impose its will through military operations beyond its borders.

A nation under siege is different in so many ways than a nation that can project its military might through the use of expeditionary conquest.  This difference is true in so ways that we cannot imagine because for so long this nation has been an expeditionary power for almost three generations.

After Hannibal, Rome depended more on its navy to transport troops in war and goods and services in peace.  Colonists in pre-Hannibalic Rome served as first lines of defense against Samnite or Gaullic incursions.  Colonists post-Hannibal brought luxuries and wealth.  Further the experience of Hannibal changed the Romans forever.

A parent imprints their person, their character, their nature in part through discipline, pain and correction.  In a sense, the greatest Roman who perhaps ever lived was never a Roman at all for Hannibal inflicted many losses in blood and treasure against the Romans that the Romans adopted Hannibal's person, their character, their nature.  They sacked cities, enslaved entire populations, they engaged in theft and rapine with reckless abandon.  Just as Hannibal did against them.

The practice of total war, war without mercy or humanity that Hannibal engaged with the Romans while NOTABLY exempting Rome's allies meant that Romans did not make treaties of equality with conquered or subjected powers.  Instead Romans sent an army and so many armies.  These armies would conquer and thus become rich off the spoils and then the Senate would appointed a governor who with the publicans (professional tax farmers) to go off an extort the province for more money.
In common parlance, it just too good to be bad.

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