Lets talk about the Monte Carlo simulation of forward rates in Euler discretization scheme under the $T_N$-forward measure, a so called terminal measure. Suppose that we have a number of time steps parameter in the Monte Carlo simulation which calculates the time step as $$dt = \frac{T_{N-1}}{\mbox{num of steps}}$$ The fixing time $T_{N-1}$ of a terminal rate is always divisible by $dt$ by construction, so there are always integer number of time steps required to reach $T_{N-1}$. However we cannot be sure about the same property for all the non-terminal rates with fixing times $T_1, \ldots, T_{N-2}$ since it may happen that $T_j$ is not divisible by $dt$ for some $j$ and so the simulation of $F_j$ spanning $[T_{j-1}, T_j)$ will stop at some $t_j$ such that $t_j < T_{j-1} < t_j + dt$ while the real fixing of this rate should have happen at $T_{j-1}$.
Is it bad? Should one always choose a time step $dt$ such that all fixings $T_{1}, \ldots, T_{j-1}$ are divisible by $dt$? Should one employ different time steps $dt_i = \frac{T_{i-1}}{\mbox{num of steps}}$ for different rates? The later seems to require an introduction of a different discretization scheme.
