Here is a sentence:
The major forces outside of the organization that have the potential to significantly influence the likely success of the products and services.
Is the use of the bold 'of' right in the above sentence?
Here is a sentence:
The major forces outside of the organization that have the potential to significantly influence the likely success of the products and services.
Is the use of the bold 'of' right in the above sentence?
It is acceptable, especially in American English. Arguably, however, omitting the of would be more standard and universally acceptable.
Two preliminary remarks
As Hot Licks has commented, your example would not normally be considered a 'sentence', because it lacks a finite verb. Rather, what you have written is a noun phrase.
As JeffUK has commented, the question is indeed a duplicate of this question.
As far as grammar
From CGEL, p. 639:
Outside takes of rather than an NP [noun phrase] when the meaning is "except" (Outside of us two, no one knew what was going on), but with the locative sense of is again restricted to AmE (%outside of Boston).
In published literature
Both phrasings are widespread in published literature, e.g.
Unfortunately, little systematic advice is available on how to choose a competent OD professional, whether from inside or o̲u̲t̲s̲i̲d̲e̲ ̲o̲f̲ ̲t̲h̲e̲ ̲o̲r̲g̲a̲n̲i̲z̲a̲t̲i̲o̲n̲.
An internal auditor may face the dilemma of considering whether to communicate the information to persons o̲u̲t̲s̲i̲d̲e̲ ̲t̲h̲e̲ ̲n̲o̲r̲m̲a̲l̲ ̲c̲h̲a̲i̲n̲ ̲o̲f̲ ̲c̲o̲m̲m̲a̲n̲d̲ or even o̲u̲t̲s̲i̲d̲e̲ ̲t̲h̲e̲ ̲o̲r̲g̲a̲n̲i̲z̲a̲t̲i̲o̲n̲.
In usage manuals
Usage manuals traditionally recommend omitting the of. Thus Garner's Modern American Usage says
outside of is inferior to outside—e.g.: "Italian goods have done well outside of [read outside] the Continent because the lira has fallen 15% vs. the U.S. dollar in the past year." ... When outside of appears in the sense apart from or aside from, either of those phrases would be more serviceable—e.g.: "Outside of [read Apart from or Aside from] economies of scale in purchasing and merged back-room operations, Pillowtex reaps Fieldcrest's well-known brands in sheets, comforters, [and] towels."
Similarly, Oxford Dictionaries says the following:
Outside of tends to be more commonly used in the US than in Britain, where outside usually suffices, but, like its cousin off of, it is colloquial and not recommended for formal writing. The adverb outside is not problematic when referring to physical space, position, etc. (I'm going outside), but the compound preposition outside of is often used as a colloquial (and often inferior) way of saying except for, other than, apart from (outside of what I just mentioned, I can't think of any reason not to). Besides possibly sounding more informal than desired, outside of may cause misunderstanding by suggesting physical space or location when that is not the point to be emphasized, or when no such sense is intended—consider the ambiguity in this sentence: outside of China, he has few interests. Does this mean that his primary interest is China? Or does it mean that whenever he is not in China, he has few interests?