The spectral properties of the inhomogeneities of the microwave background on Planck multi-frequency maps that are distant from the sources of the RCR catalog by the half-width of the power beam pattern of the high-frequency Planck complex (+/-2.5 arcmin), as well as the spectral features of the sources depending on the presence of positive spots near them, are studied. About 830 objects of the catalog were examined for the detection of spots with positive amplitudes near them. The features that indicate the connection of positive peaks on the Planck maps with the nearest radio sources are revealed. First, it is the excess of the number of RCR sources with flat and normal spectra, near which there are spots, over the number of sources with steep spectra. Secondly, the number of spots with positive amplitude on Planck maps that coincide within +/-2.5 arcmin with the coordinates of source-free areas on NVSS, FIRST maps and have the same sizes is on average almost one and a half times less than the number of spots that coincide with RCR objects. It is shown that RCR objects, near which there are no spots, have steeper spectra compared to the spectra of sources, near which spots are detected. The distribution of the spectral indices of spots in the range of 30--217 GHz was close to the distribution of the spectral indices of RCR sources in the range of 100MHz-8.5GHz and their median values almost coincided. This may indicate that the positive fluctuations on the Planck maps detected near RCR objects in the range of 30-217GHz are synchrotron in nature and may be associated with these objects. They can be manifestations of these objects or manifestations of their host galaxies and their environment in the submillimeter range. In the range of 353-857GHz, some of the detected spots can be classified as dusty. The spectra of RCR sources, near which such spots were detected, were steeper than the spectra of RCR objects, near which spots were detected only in the frequency channels 30-217GHz. The steeper the spectrum of the RCR object in the range of 100MHz-8.5GHz, the greater the value of the positive spectral index of the nearest spot in the range of 353-857GHz. The spots, whose two-frequency spectral indices indicate their dusty nature, may be associated with the high dust content in the host galaxies of RCR objects and the processes of star formation in them. It is also possible that the rise in the spectra at high frequencies may be caused by the presence of a signal from cold galactic dust on the frequency maps.