The lock screen, and the top bar itself both show the time a little weird in Japanese.

The lock screen will have, for example: 火曜日10月２３ Tuesday(火)of the week(曜日) 10 month(月) 23 (with nothing after it).

It isn't correct this way to have nothing after the date. The most common way to write month, day, day of the week all out would be to have

10月23日(火) ie 10(month) 23(day) followed by just the first character for the day of the week, perhaps in brackets.

With the year would be: 2017年10月23日(火)

(if using the Western year reckoning, as is frequently done but not always)

The lack of 日 after the date is not correct.

Full disclosure, I'm an Irish-descended Canadian but I lived and worked in Japan for eight years and not once on a computer, calendar, chalk board, appointment book, shop sign, train schedule, or scrawled note did I ever see a date written in 火曜日10月２３ format.

Though if you are just referring to a Tuesday in a sentence, you will definitely see and say 火曜日 (kayoubi, you'd never just say ka). If you're writing it out as part of the full date (year, month, day) then 9.9 times out of 10 you'll just use the first character (火), akin to seeing just Sun Mon Tue Wed Thu Fri Sat (日月火水木金土), again, in this format: 2017年10月23日(火). Year, month, day, day of the week.

Thoughts?