what we see now is a huge political mess
I fail to see such any such huge mess to be honest. Iran's situation was no less challenging in the 80's, when she had to end the war imposed by Iraq in a manner which Imam Khomeini likened to "drinking from a chalice of poison".
In fact, in many ways Iran appears to be more secured today than it was back then. Imam Khomeini's exceptional leadership of course prepared the ground and made Iran's current position possible. Imam Khamenei then successfully built upon that strong foundation.
caused by lack of a strong leadership and corruption that has nested even in the office of the leader himself (without his knowledge).
Have no doubt that if Khomeini continued to rule up until the 2000's the situation would have been totally different.
Imam Khamenei is not weaker than his predecessor. What has changed are the rules of the game, as well as the internal and external context. These are factors outside the Supreme Leader's ability to determine, he must cope with them.
Now some of these historic evolutions turned out to be favorable to Iran, others less so. It isn't a black & white picture.
Given a comparable context, Imam Khomeini would not have acted much differently than current Supreme Leader Khamenei. In fact ayatollah Khamenei is the ideal successor to Imam Khomeini: he's the only one from his generation capable of best prolonging Imam Khomeini's political heritage, both ideologically and practically.
One cannot appreciate the issue while remaining oblivious to history and context. In this regard, it cannot be stressed enough how two factors which prevailed in the 1980's simply do not apply any longer, and this has nothing to do with ayatollah Khamenei's decisions and policies, since we are talking about general historical factors that escape any one person's control:
1) The fully fledged, 8-year war imposed on Iran by Saddam's Iraq with support from virtually the entire planet. One cannot compare a context of ongoing conventional war with a peacetime situation, especially when as far as the effective political prerogatives and power of the Leadership are concerned. War considerably increases the Leadership's margin of action.
2) Revolutionary fervor. Every society that experienced a popular revolution with time witnessed the same relative slowing down in mobilization and fervor. This too has nothing to do with who is in charge and would have taken place anyway. Look at China: in order to revive the flame so to speak, it took a decade-long (mid 60's to mid 70's), concerted push from the central government which came to be known as the Cultural Revolution, with debated results. Of course being in charge during an early revolutionary period will naturally enhance a leader's autority, irrespective of said leader's political choices or governing style.
This being said, it's interesting to note that except for shahid Rajai (whose presidency was quite short-lived) and ayatollah Khamenei himself, all presidents of the Islamic Republic, encouraged by the popular vote their mandates rest upon, ended up perceiving themselves as some sort of political rivals to the Leadership and thus proceeded to challenge the authority of the Supreme Leader (even if this is not done all too openly). Not content with the extent of the presidency's constitutional mandate, they attempted to overstep it. The case of Mohammad Khatami is a special one: while Khatami did adhere to ideological positions which challenged the guidelines set by the Leadership, he did not have the same type of personal ambition as Rafsanjani, Ahmadinejad and Rohani in trying to confront the Supreme Leader. This is what Dariush Sajjadi, journalist and former advisor to Mehdi Karoubi, has termed "the trap of democracy" ("tale-ye demokrāsi").
Apart from shahid Rajai, only ayatollah Khamenei during his presidency staid truly and fully loyal to the general line and concrete precepts defined by a Supreme Leader of the Islamic Revolution. Therefore he was and is closest in spirit and practice to Imam Khomeini.
I also very much doubt that ayatollah Khamenei isn't well informed about what is going in his country, let alone inside his office. Actually his speeches show he is one of the best informed persons in Iran.
Khomeini delivered a strong, united IR to Khamenei and the latter will deliver a divided system to his successor.
Oh there were political faultlines under Imam Khomeini alright.
Rivalries used to be such that the credentials of outright heroes of the Revolution and Sacred Defence such as shahid Mostafa Chamran, were openly and publicly questioned by some officials. At the Majles, controversial issues were so hotly debated that representatives at times went as far as throwing chairs at each other (at least that's what one of them claimed back then).
For all it's stability, the Islamic Republic in the 80's couldn't prevent considerable domestic challenges such as the terrorist killing of an elected president (shahid Rajai), the deviation of another one (Bani Sadr), the bombing of the Islamic Republican Party's headquarters resulting in the martyrdom of numerous leading figures of the Revolution such as ayatollah Beheshti, other terrorist attacks against historic greats of the Revolution such as shahid Qoddusi, and so on. Much of this was enabled by the survival of a stay-behind network amidst the Iranian intelligence and security apparatus, network which had been set up prior to the Revolution by SAVAK officer Parviz Sabeti (now a resident of Isra"el") in coordination with the zionist regime's Mossad (similar to NATO's Gladio networks), as explained by Pour-Massoud in his excellent speeches.
As for the emergence of the reformist faction, let's not forget that the centrist pragmatics led by hojjat al-lslam Hashemi Rafsanjani already used to play a comparable (although not fully identical) role under Imam Khomeini. Of course centrists and reformists will deny this, but principlist review of history suggests that the Imam's decision to agree to the 1988 ceasefire did not merely result from the situational evolutuion on the battlefield, but also from domestic pressures exerted by certain (read so-called pragmatist) quarters.
Nor should it be forgotten that the genesis of the reformist faction, that is in fact the conversion of the so-called Islamic left away from its originally held anti-imperialist / anti-colonial, revolutionary authoritarianist, cultural conservative and quasi-socialist economic positions, towards cultural, political and economic liberalism coupled with a western-apologetic outlook on foreign policy, occurred largely as a consequence of the Mehdi Hashemi affair as well as of ayatollah Montazeri's falling from grace, both of which actually unfolded in the 80's.
In conclusion, both Imam Khomeini and Imam Khamenei have unquestionably been outstanding leaders who equally safeguarded Iran's sovereignty and who equally contributed to strengthening Iranian resistance against global oppressors. In the evolved historical context within which he has to act, Supreme Leader Khamenei's work is a perfect continuation of Imam Khomeini's founding effort. It is really hard to imagine that anyone else would have been more successful in this endeavour.
On a closing note, I would absolutely recommend any Persian-speaker interested in these questions to watch the extraordinary documentary "Qaem Magham" made in Iran a few years ago about ayatollah Montazeri, as it sheds renewed light on many aspects of the history of the Islamic Republic:
