It's a play on words.
When talking about the colour of the clothes, the natural reading of "a few shades off" is to associate shades with colour and off with accuracy - that is, the clothes were not quite the correct colours to represent patriotism.
When using the same expression to describe the day, the following definitions come into play:
A shade —— (phrase) A little ——: ‘he was a shade hung-over’ ‘It was a shade less than the champions deserved.’ - ODO
Off adjective 1 [attributive] Characterized by performing or feeling worse than usual; unsatisfactory or inadequate: ‘even the greatest athletes have off days’ - ODO
The natural reading is then that the day seemed a little less satisfactory than the author would expect for an inauguration.