The wordy phrase in the midst of could almost always be shortened to amid, among, during, or in (or, for non-U.S. writers, amidst). In some cases, the phrase could be removed outright. There’s nothing strictly incorrect about using in the midst of, though, so use it if you think it sounds better than the alternatives.
There are shorter alternatives to in the midst of in each of these cases:
In the midst of [Amid?] the Great American Royal Wedding Frenzy, it’s hard to remember that not everything British is upscale and quaint. [Los Angeles Times]
Yet more proof that we’re in the midst of [in?] a TV golden age. [Atlantic]
In the midst of [During?] a riotous wake at the Pink Hotel, a 17-year-old London girl takes clothes and a suitcase from her dead mother’s room. [Daily Mail]
And in the midst of could be removed outright from these sentences:
I had the opportunity to connect with Jeffrey Gitomer recently, as he was in the midst of promoting his new book called Social Boom!. [Forbes]
North Shore model-actress Nicola Simpson has modelled for Christian Dior, Elle and Adidas and is in the midst of filming the next series of American TV hit Spartacus. [New Zealand Herald]