  Let $G$ be a discrete group with property (T). It is a standard fact that, in
a unitary representation of $G$ on a Hilbert space $\mathcal{H}$, almost
invariant vectors are close to invariant vectors, in a quantitative way. We
begin by showing that, if a unitary representation has some vector whose
coefficient function is close to a coefficient function of some
finite-dimensional unitary representation $\sigma$, then the vector is close to
a sub-representation isomorphic to $\sigma$: this makes quantitative a result
of P.S. Wang [Wa]. We use that to give a new proof of a result by D. Kerr, H.
Li and M. Pichot [KLP], that a group $G$ with property (T) and such that
$C^*(G)$ is residually finite-dimensional, admits a unitary representation
which is generic (i.e. the orbit of this representation in
$\mathrm{Rep}(G,\mathcal{H})$ under the unitary group $U(\mathcal{H})$ is
comeager). We also show that, under the same assumptions, the set of
representations equivalent to a Koopman representation is comeager in
$\mathrm{Rep}(G,\mathcal{H})$.
