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Solar observations with the Atacama Large Millimeter/sub-millimeter Array (ALMA) facilitate studying the atmosphere of the Sun at chromospheric heights at high spatial and temporal resolution at millimeter wavelengths. ALMA intensity data at mm-wavelengths are used for a first detailed systematic assessment of the occurrence and properties of small-scale dynamical features in the quiet Sun. ALMA Band 3 data (~ $3$ mm / $100$ GHz) with spatial resolution ~ $1.4$ - $2.1$ arcsec and a duration of ~ $40$ min are analysed together with SDO/HMI magnetograms. The temporal evolution of the mm-maps is studied to detect pronounced dynamical features which are connected to dynamical events via a k-means clustering algorithm. The physical properties of the resulting events are studied and it is explored if they show properties consistent with propagating shock waves. For this purpose, observable shock wave signatures at mm wavelengths are calculated from one- and three-dimensional model atmospheres. There are 552 dynamical events detected with an excess in brightness temperature ($ΔT_\text{b}$) of at least $\geq 400$ K. The events show a large variety in size up to ~ $9$ arcsec, amplitude $ΔT_\text{b}$ up to ~ $1200$ K with typical values between ~ $450$ - $750$ K and lifetime at FWHM of $ΔT_\text{b}$ between ~ $43$ - $360$ s, with typical values between ~ $55$ - $125$ s. Furthermore, many of the events show signature properties that suggest that they are likely produced by propagating shock waves. There are a lot of small-scale dynamic structures detected in the Band 3 data, even though the spatial resolution sets limitations of the size of events that can be detected. The amount of dynamic signatures in the ALMA mm data is very low in areas with photospheric footpoints with stronger magnetic fields, which is consistent with the expectation for propagating shock waves.