Problems in some parts of Monique Hakim thesis? In "Reminiscences of Grothendieck and his school" Luc Illusie says:
"I heard from Deligne that there were problems in some parts. (of Monique Hakim thesis).
Topos annelés et schémas relatifs, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 64, Springer, Berlin, New York (1972).
My question is for a reference for these "problems". What are the problems? Where?
 A: I have no idea if it's what Illusie and Deligne are referring to, but W. D. Gillam points out some strange behavior of Hakim's Spec functor in Remark 11 of this paper. Gillam says that "there is no meaningful situation in which Hakim's Spec functor agrees with the 'usual' one," and that "if $X$ is a locally ringed space at least one of whose local rings has positive Krull dimension, Hakim's sequence of spectra yields an infinite strictly descending sequence of [morphisms of ringed spaces] $\cdots\to\text{Spec}(\text{Spec}_{\ \!}X)\to\text{Spec}_{\ \!}X\to X$."
A: The published version of the paper (it is free), yet apparently not all versions in circulation, has a footnote on that sentence: 

(13) Added in April 2010: Deligne doesn’t think there was
  anything wrong but remembers that the objects she
  defined over analytic spaces were not the desired ones.

Thus, it seems there is no direct problem.
The bibliographic details are (the relevant part is on page 1110, fifth page of the pdf): 
Luc Illusie, Alexander Beilinson, Spencer Bloch, Vladimir Drinfeld, and et al., Reminiscences of Grothendieck and his school, Notices Amer. Math. Soc. 57 (2010), no. 9, 1106--1115. 
