It seems that Robinson addressed some gross mistakes that happend in the early times of calculus and that were passed with silence by the posterity, the inventors of more rigor in analysis, in particular Weierstraß and his school. To give few examples:

Leibniz, Jakob Bernoulli, and Euler accepted

$\frac{1}{1-(-1)}= 1 - 1 + 1 - 1 +-... = \frac {1}{2} $

Leibniz subtracted two harmonic series, with the correct result though,

$\sum_{k \geq 2}^{\infty} \frac{1}{1-k^2} = \frac{1}{2} \sum_{k \geq 2}^{\infty} \frac{1}{k-1}  - \frac{1}{2} \sum_{k \geq 2}^{\infty} \frac{1}{k+1} = \frac{3}{4} $

but in a way that today certainly would not be tolerated.

Wallis and Euler accepted

$\frac{1}{1-2}= 1 + 2 + 4  + ... = \frac {1}{-1} > \frac {1}{0}  > \frac {1}{1}  $

Euler calculated

$1 + 2 + 3  + ... = \frac{-1}{12}$

which, irrespective of the analytic continuation of the $\zeta$-function and Ramanujan's rediscovering it, is as wrong as the sum of the geometric series above.

With respect to such mistakes, those of d'Alembert, touched in a comment by the author of this question, seem to be negligible. In my opinion they are not the target of Robinson's remark. Some gaps in d'Alembert's proof of the fundamental theorem of algebra have been remedied by Gauss. However, even Gauss left gaps in his first proof. And nobody knows what future generations will have to criticize in proofs that presently are accepted as complete. Further d'Alembert held the opinion that irrationalities are not numbers. But that has to be understood out of his time where "number" denoted a string of digits that can be read from a sheet of paper.