Reconfigurable intelligent surface (RIS) has recently been envisioned to provide an adaptable channel for futuristic wireless communication networks. This work characterized the impact of hardware impairments in the downlink RIS-aided non-orthogonal multiple access (NOMA) wireless networks. We considered the hardware impairments in the transceivers of the base station (BS) and users, phase error at the RIS and the imperfect successive interference cancellation (SIC) for the NOMA users. Specifically, the performance is evaluated by deriving the closed-form expressions for the outage probability (OP), spectral efficiency (SE) and energy efficiency (EE). Additionally, the performance of the orthogonal multiple access (OMA) system is also evaluated and compared with its NOMA counterpart. The RIS-aided NOMA outperforms OMA for the ideal hardware scenario. However, the hardware impairments significantly deteriorate RIS-aided NOMA's performance compared to RIS-aided OMA. Further, we have also compared the proposed RIS-aided NOMA with the baseline full-duplex relaying (FDR) based NOMA. The results show that the gains are more significant for a RIS-aided system than FDR.