There are two common notations for Omaha-Ponca speech: the old one used by Dorsey (cf. Dorsey 1890: 4-8), and the one introduced by Fletcher and LaFleche (1911), which was adopted by the Omaha people as a more practicable notation. The problems with Dorsey's notation are that it is far too detailed phonologically, that it is partly redundant, and that is uses a very large set (79 symbols!) of in great part 'exotic' special characters (though based on Latin characters), which are difficult to replicate — and that makes Dorsey's notation impracticable. As a historical linguistic documentation however it is valuable due to the preservation of all this detail — it might prove useful especially for etymologists. The Fletcher/LaFleche, (or modern, or practical) notation uses only two uncommon characters, and those are superscript n (ⁿ) for nasal vowels and superscript h (ʰ) for aspirated stops, otherwise relying entirely on basic Latin symbols.

A language orthography doesn't need to provide a full phonetic description: it is part of the job of the literate speakers, to fill in the phonetic blanks from knowledge of pronunciation rules and irregularities. Music notation, for example, only provides certain structural and elementary information on tempo and mood, and yet a musician or an orchestra can reproduce an incredibly rich form of the piece in question. A notation is a code, which is necessarily spartan; poor, compared to what it stands for. But its role is only to stimulate the brain of an accordingly trained reader in a certain way, in order to reproduce a whole richly faceted world of content. It is not just the text (or musical score, or other types of notation used by humans) that carries the information. It is always the text (the stimulus) in conjunction with the reader, the latter who re-builds and builds the information, guided by the stimulus. It is the reader who uses his whole knowledge of the world and of language to reproduce the world of the writer.
However, some content will be inevitably lost or remain subject to interpretation. A good notation system has to make a compromise between usability (i.e. simplicity) and informational capacity (i.e. complexity, detail).

As for the modern Omaha-Ponca notation system I see two minor shortcomings, or weaknesses.

1.  The notation of nasal ɔ

The nasal aⁿ [ã] in Dorsey is changed to oⁿ [õ] in Fletcher/LaFleche's notation. This is due to the fact that neither a nor o reflect the phonetic nature of the sound, which is an intermediate between them, namely ɔ (like in English 'top', 'flop', 'crop'), as a nasal therefore ɔ̃. The notation of either aⁿ or oⁿ influences the way the words' acoustic character is perceived by readers and might in the long term change the language itself. On the other hand, English readers have no problems by discerning between pronunciation of e.g. 'top' and 'more', so maybe the current notation of ɔ̃ as oⁿ might only be a problem for non-speaker readers.

2.  The loss of ŋ

Another shortcoming is the unified nasal notation oⁿ (modern) for and aⁿ in Dorsey, which are in my view significantly different: stands for [ɔŋ], in which the open-mid back vowel is followed by a velar nasal, while aⁿ stands for [ɔ̃], a nasal vowel.

In older notations of Lakota, nasals are represented as nasal vowels, like for example ą, ų. In Boas/Deloria (1941: 69) 'dog' is transcribed as šų´ka, in Rood/Taylor 1996 similarly as šų́ka, while in the New Lakota Dictionary (2008,2011: 516) nasals are marked by ŋ following the vowel, thus šúŋka 'dog'. The example of current Lakota writing offers a good solution to differentiate between pure nasal vowels (e.g. [ã]) and nasal vowels fading out in a velar nasal (e.g. [ãŋ]) — whereas it's true that Lakota goes the one other way and uses the ŋ-nasal notation only.