1) 1993 constitution crisis. Role of the president had gained more power compared to the State Duma (lower legislative house).
2) Privatization in Russia was a mess. On one hand, it created the oligarch class, which led to the obvious money → political power transition. On the other, huge slice of society had suffered economically, which explains the mid 2000s social contract of "People get less democracy in exchange for economical stability".
3) KGB archives hadn't been opened when there was an opportunity to do so. It was a huge mistake.
4) Re-election of Yeltsin in 1996 was against the natural way of events. Lots of resources were used in agitation, including, but not limited to professional political consultants from the USA. Putin's cronies were learning from the best ones.
5) As of 1999, Putin's appointment was a collective decision between two oligarch clans. It was a pure feudalistic/mafia-like process, without a hint of democratic principles. By the time of the next president elections, ruling oligarch clan controlled most of the media.
That's a very oversimplified view. First Chechen war is not mentioned. Role of the Second Chechen war in Putin's presidency is important, yet not crucial.