It's an unfortunate fact of nature that the Earth takes slightly more than 365 days to go around the Sun, and so our Earth year is not readily decimalized.
However, our present calendar makes more of a mess of the situation than is necessary. Our months are unequal in length and contain a non-integral number of weeks. We need a printed calendar to associate a day of the year with a day of the week.
Fixing these problems is probably infeasible because changing the calendar would be vastly expensive (much worse than the fuss over Year 2000). However, just for fun, I give you two proposals for a more sensible calendar.
The Cotsworth proposal
Moses Bruine Cotsworth (born 1859) proposed a year divided into 13 months of 28 days each. Each month starts on a Sunday, and (for instance) the 16th day of any month is always a Monday.
Cotsworth suggested calling the extra month Sol, and putting it between June and July.
As well as the 13 months, each year has one spare day, or two in leap years. These are not assigned to any month or to any day of the week, and could be associated with national holidays (for instance, Cotsworth suggested Christmas Day).
This proposal solves the main problems of the existing calendar. I think the main disadvantage is that 13 months can't be divided neatly into quarters, as companies are accustomed to do.
As an alternative, I propose dividing the year into 12 months of exactly 30 days each, and deleting one day of the week, so that each month consists of exactly five 6-day weeks. (I think three 10-day weeks would be less acceptable.)
There are five or six spare days in each year, which could be assigned to national holidays. I'd suggest putting them at the end of every other month. In accordance with tradition, the one at the end of February could be omitted in non-leap years.
The year now contains 60 weeks instead of 52, which is an improvement because 60 is a more convenient number, being divisible by 2, 3, 4, and 5.