"Things" means everything, including sights (material forms), sounds, smells, tastes & touches and the whole universe. Therefore, in the phrase: "Sabbe dhamma anatta ti", the translation of "things" or "phenomena" is appropriate; where things includes everything, including Nibbana.
But the word 'dhamme' contained in the sense sphere triad of mano (mind sense organ), mind-consciousness (mano-vinnana) and mind-objects (dhamme) means "mind-objects", namely, feelings, perceptions, thoughts, defilements, mental images & Nibbana.
Therefore, the word 'dhamme' in Dhammpada 1 as well as in the 6th sense sphere triad is generally held to not mean 'things' but, instead, "mental states" & "mind-objects". However, the word 'dhamma' can also mean "practises" (e.g., AN 10.15; AN 10.58), both unskillful & skillful.
Personally, I cannot confidently suggest how the word 'dhamma' should be translated in Dhp 1 however I can confidently suggest it does not mean 'things' or 'phenomena' because this simply appears alien to the context, which is about intention & kamma and results (vipaka).
Also, as mentioned, the word for mind is "mano" rather than "vinnana". The word "mano" implies the intellect or decision making is operating rather than mere sensory experience of consciousness (vinnana).
It is Buddhism 101 to know the word 'dhamma' can be translated in numerous ways dependent upon the context. For example, when Upatissa (Sariputta) asked the arahant Assaji: "Under whom, friend, have you gone forth as an ascetic? Who is your teacher and whose doctrine (dhamma) do you profess?" or when the Buddha used the term 'Dhamma-Vinaya', the word 'dhamma' here obviously does not mean 'thing'.1. Mano precedes all dhammā. Mano is their chief; they are all mano-wrought. If with an impure manasā a person speaks or acts suffering follows him like the wheel that follows the foot of the ox.
2. Mano precedes all dhammā. Mano is their chief; they are all mano-wrought. If with a pure manasā a person speaks or acts happiness follows him like his never-departing shadow.