I should point out that UTC didn't begin until 1960...
The 28 minutes jump is likely Iceland coming into alignment with GMT, for much the same reasons as Ireland did; to improve trade and commerce in a world now using telegraphs, telephones and trains. We're ok becoming disconnected from mean solar time in order to connect more with each other.
Samoa skipped a day in 2011, jumping from UTC−11:00 to UTC+13:00, so that it could align with Australia and New Zealand, its biggest trading partners -- so Australia's Friday is also Samoa's Friday.
We'll always have discontinuities in civil timekeeping, as it's there to serve the whims of humans, not the other way around.