“We suffered no other inconvenience but that arising from the dust.” This is incorrect. After other we should use than. Therefore, “We suffered no other inconvenience than that arising from the dust.”
After else, other, rather, and all comparatives, the latter term of comparison should be introduced by the conjunction than.
Either the
“Passengers are requested not to converse with either conductor or driver.” This is one of those business notices that are often more concise than correct. It implies that there are two conductors and two drivers. The sentence should read, “Passengers are requested not to converse with either the conductor or the driver.”
Lest, That
“I feared lest I should be left behind.” Use the copulative that, and not the disjunctive lest. “I feared that I should be left behind.”
Otherwise than
“He cannot do otherwise but follow your direction.” Use than, not but, after otherwise. Hence, “He cannot do otherwise than follow,” etc.
After that
“After that I have attended to the business I will call upon you.” The word that is superfluous.