Yes, kiel can cause ambiguity ...
The sentence
Kiel la administranto de la korporacio, mi pensas, ke li eraras.
is indeed ambiguous and, as you state, can mean either
As the manager of the corporation, I think he is wrong.
(i.e., the speaker is the manager and makes is judgement in that capacity)
or
(Just) like the manger of the corporation, I think he is wrong.
(i.e., the speaker isn't the manager, but shares the manager's opinion on that matter)
... but often, it can be resolved by context
So how can one distinguish these two senses?
Usually by context. A phrasing like this would usually be used if the speaker expects the audience to already know whether the speaker is the manager of the corporation, or whether that's another person.
Of course, like in other languages, it can happen in Esperanto that an ambiguous sentence is used in a situation where the ambiguity cannot be resolved by context, e.g. due to the speaker not being aware of the ambiguity, or due to the speaker making wrong assumptions about what's already known to their audience (or because they don't care.) Like in other languages, the audience would have to ask for clarification if it wants to know what meaning was intended.
Alternative, less ambiguous phrasings
Or are there any other words to distinguish the two meanings more specifically?
I can't come up with any Esperanto phrasings that carry one of the meanings exactly without the other, but preserving the other connotations (or lack thereof) of the original phrasing. But if we allow some flexibility in the semantics, there surely are alternatives.
The speaker is the manager
As the manager of the corporation, I think he is wrong.
This can have different connotations / implications even in English, e.g.:
I think he is wrong. And because I'm the manager of the corporation, my opinion on this should matter.
or
Due to the insights I gained as the manager of the corporation, I think he is wrong.
For the first connotation variant (without spelling it out by just translating that interpretation to Esperanto), simply dropping the "kiel" and using "la administranto de la korporacio" as a defining clause for the subject "mi" might work:
Mi, la administranto de la korporacio, pensas, ke li eraras.
For the latter connotation variant, dropping the definite article "la" can work:
Kiel administranto de la korporacio, mi pensas, ke li eraras.
or
Mi, kiel administranto de la korporacio, pensas, ke li eraras.
But only if it's known that the corporation has only one manager. Otherwise, this could also be interpreted as
(Just) like a manger of the corporation, I think he is wrong.
I'm unsure what the best phrasing would be if the number of managers has to be assumed to be unknown to the audience.
The speaker isn't the manager
You can express "Both, the manager [...] and me, think that ...":
Kaj la administranto de la korporacio(,) kaj mi pensas, ke li eraras.
I'm unsure whether "ankaŭ" could also help. Modifying "me" with it could remain ambiguous if it's possible that it may refer to another previously mentioned person than the manager:
Kiel la administranto de la korporacio, ankaŭ mi pensas, ke li eraras.
could probably be read as either
As the manager of the corporation, I, too, think he is wrong.
(implying that the speaker is the manager and agrees with someone previously mentioned)
or as
(Just) like the manger of the corporation, I think he is wrong.
Having "ankaŭ" modify "la administranto" could maybe work, though:
Kiel ankaŭ la administranto de la korporacio, mi pensas, ke li eraras.
But I'm very unsure how idiomatic / well-styled and how comprehensible that is.