The lamellar cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (Tc), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa2CuO4+δ (Hg1201) is a single-CuO2-layer cuprate with a particularly high optimal Tc and a simple crystal structure, yet there exists little information from ARPES about the electronic properties of this model system. Here we present an ARPES study of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales: a subgap low-energy kink, an intermediate-energy kink near 55 meV, and a peak-dip-hump structure. The first two features are attributed to the coupling of electrons to Ba-derived optical phonons and in-plane bond-stretching phonons, respectively. The nodal peak-dip-hump structure appears to have a common doping dependence in several single-layer cuprates and is interpreted as a manifestation of pseudogap physics at the node. These results establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material and in terms of connecting comparable spectral features in multiple structurally similar cuprates.