The only effect is heating. Microwaves are non-ionizing radiation which means they do not break chemical bonds. Microwaves have an energy of about 10^-5 eV. Ionizing radiation is defined by the FCC to start at 10 eV (molecular bond energies are usually 1-10 eV per bond, and 10 eV corresponds to 124 nm ultraviolet). The EPA definition is that ionizing radiation starts at 33 eV (the ionization energy for a molecule of water). Either way, 10^-5 eV is well under this limit.
Being under the limit doesn't mean that it takes more radiation to be ionizing, it means that it is never ionizing. If the energy of the photons is below this limit, then no amount of exposure will make it ionizing (unless you receive so much that you become so hot that you turn into a fine plasma, but people do not get vaporized when they turn on their cell phones' Bluetooth or stand next to their 2.4 GHz Wi-Fi router). You can't increase photon energy just by increasing the number of photons.
As long as your body is able to dissipate heat faster than it accumulates it, there are no negative effects whatsoever. For non-ionizing radiation, the test for whether it is harmful is easy: Are you burning or overheating due to radiative heating? Then you're receiving too much radiation. Otherwise it's fine.
Could there be unknown effects? Maybe, but there is no reputable research which shows any negative effects. The slight tissue heating you receive from the 2.4 GHz Wi-Fi or Bluetooth signals from your phone is dwarfed by the amount of tissue heating caused by your muscles holding the phone up.