The simple normal linear model (for a single explanatory variable) can be easily extended with extra terms for further explanatory variables.
This model and data can be represented in 3 dimensions if there are only two explanatory variables but cannot be fully displayed if there are more. It is therefore more important that residual plots and regression diagnostics are used to check for problems with the model.
Interaction and multicollinearity are potential problems in multiple regression models that have no counterpart if there is only a single explanatory variable. It is important that they are considered when analysing multiple regression data.