Measuring transmitter power, do and don't

I usually see measurements of power of HF transmitters using just a common power meter (broadband coupler and diode inside). Please tell me if my next thoughts are correct:

Since these power meters are broadband, and they have just a needle analogue meter to measure power (non selective), they not only measure power of the carrier, but the total power of the carrier plus the transmitter harmonics. If the transmitter output is not filtered, false readings (higher) would result from such measurements.
Unless a selective volt meter or a spectrum analyzer is used, actual power of the carrier (thus ignoring harmonics power) cannot be made.
If an effective LPF is used at the transmitter output, then the total measured power from a common power meter will be close enough to the actual carrier power, since harmonics will be much attenuated.
One way to measure power with the scope (assumming a harmonics-free signal), from a 50R transmitter, is to terminate the transmitter with a 50R non-inductive dummy load and then measure the voltage accross this load, from the 1M scope port (not the 50R!). The power measurement then will be done like directly measuring with a a scope having an input of 50R.
    Please tell me if my thoughts are correct on each of the above points.

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Yes, you are right in all points. A good transmitter should have a LPF at its output to attenuate harmonics, then a power meter will indicate only the desired carrier power.
Using a power divider is also correct, and all its ports should be terminated in 50 Ohms. The oscilloscope input is often 1 MegaOhm, so a 50 Ohm termination should be attached.
The best method combines the power divider with a calibrated spectrum analyzer, so you can measure reliably the desired carrier power as well as the harmonics (and other possible spurs).
Care must be taken not to exceed SA input power as this may generate harmonics and spurs.
This combination is preferable as it allows you to monitor the correct PS adjustment and load matching to an antenna or another load.