Are there any clear identifiers in speech, i.e. shibboleths, that people from former Soviet republics manifest in their speech? For instance, I've noticed that in certain former republics, they pronounce "что" as "чи-то", "шо"/"шё", while others roll their r's more forcefully and longer than in "standard" Russian.
Ukrainian Russian is the only clearly identifiable one, a language variety unto itself somewhat like Irish English (and not to be confused with the Ukrainian language in the same way you also have an Irish language, although Ukrainian is better compared to Scots in terms of similarity). A significant number of people from Kazakhstan, including ethnic Kazakhs fluent in Russian, have Southern Russian vowel patterns (сказал
[skə'zal] rather than
[skɐ'zal]), but that's not consistent. Any other differences would register as a foreign accent or, if they're minor ones, pass under the radar.
That depends on how detailed you want to be. Even a native speaker will be surprised at the variety of dialects and nuances upon opening a linguistic atlas.
The "чё" or "шо" that you mentioned are quite prevalent in speech in some regions of Russia. But the distribution isn't even, and also depends somewhat on socio-educational factors, as these variations are often considered improper by purists, if not downright wrong.
So it's not always possible to make the "clear" distinction you're looking for. That said, some dialects are easily identifiable, such as Ukrainian (Ukrainian Russian) by their fricative Ukrainian 'г' and many other characteristic features.