Is there a better, more accurate (need not be precise, just consistently accurate) source? I have considered http://www.shadowstats.com/ but it's not transparent unless you buy the service. (Nothing wrong with that but it makes it much less transparent: fewer eyeballs watching it.)
the best way to get accurate unemployment numbers is to look at the BLS report, but focus on the U6 or U5 number. The "official" number is U3 which can be manipulated relatively easily.
The Bureau of Labor Statistics also calculates six alternate measures of unemployment, U1 through U6, that measure different aspects of unemployment:
U1: Percentage of labor force unemployed 15 weeks or longer.
U2: Percentage of labor force who lost jobs or completed temporary work.
U3: Official unemployment rate per the ILO definition occurs when people are without jobs and they have actively looked for work within the past four weeks.1
U4: U3 + "discouraged workers", or those who have stopped looking for work because current economic conditions make them believe that no
work is available for them.
U5: U4 + other "marginally attached workers", or "loosely attached workers", or those who "would like" and are able to work, but have not looked for work recently.
U6: U5 + Part-time workers who want to work full-time, but cannot due to economic reasons
There is another important number to look at, that is the labor force participation rate, which shows the percentage of working age people that are employed, this is also often broken down into demographics and age ranges.