Below are some of the potential vulnerabilities of the Borei class (I and II) according to Internet sources:

The continuous running seamless hydraulic pump might become noisy within a few months to a year of operation unless replaced (it's a “plug and play” unit that has no maintenance).
High Demand Transient — certain systems might become noisy when they are under heavy load (both electrical and hydraulic).
Missile Tube Preparation — it might take up to 20 minutes to prepare the missile tubes for launch which would be as slow as the older Delta class submarines.
Motor Generator Harmonics — the PG-141M 5,500hp dc motor for lower speeds might be noisy at times and so might be the GTZA OK-9VM geared-turbine system for speeds above circa eight knots. The latter is derived from the older Oscar class and is also used in the new Yasen Class, while the dc motor hybrid component is a new design.
Station Keeping — some support systems might become noisy during station keeping. The Borei is the quietest when moving without changing course.
Hull Pop — hull number 1 might emit transient during depth changes. This was detected during torpedo/missile firing exercises and it applies only to Borei-I which uses some hull components from older Akula (Щука-Б) class subs, while Borei-II uses all new hull components.
The US Navy has intelligence on the number of vanes (blades) in the pump-jet propulsion system, which is reportedly 21. This, combined with estimates or intelligence on the vane output gear ratio, can allow them to calculate the sound frequencies emitted at various speeds and configure their sonars to search for them.