The bank's current anti-money laundering program is inadequate because it does not include a process for monitoring customer account activity, which is a key component of detecting and reporting suspicious transactions. The fact that the consultant and the bank have mutual clients does not affect the risk rating of those customers, nor does it justify a lower level of scrutiny. The bank should revise its procedures to ensure that it has a comprehensive and risk-based approach to customer due diligence, transaction monitoring, and reporting.
CAMS Certification Package - 6th Edition, Chapter 3: Compliance Standards for Anti-Money Laundering (AML) and Combating the Financing of Terrorism (CFT), pp. 67-69.
FATF Guidance for a Risk-Based Approach: Legal Professionals, pp. 10-11, 19-20.
BSA/AML Internal Audit: PwC, pp. 1-2.

Proliferation financingrefers to the act of providing financial services or funds for thedevelopment, acquisition, or delivery of nuclear, chemical, or biological weapons. The core threat involvesnetworks of individuals and entities using the financial systemto obtain sensitive technologies, materials, or knowledge forweapons of mass destruction (WMDs).
TheFinancial Action Task Force (FATF)identifies this as a major international security threat and requires institutions to assess and mitigate such risks.
Reference: ACAMS CAMS Study Guide - 6th Edition, Chapter:Sanctions and Proliferation Financing- Section:Understanding and Identifying Proliferation Risks

Conducting anonymous transactions is the most likely activity to facilitate money laundering through online banking systems with inadequate controls. Anonymous transactions allow money launderers to hide their identity, source and destination of funds, and the purpose of their transactions from the authorities and the financial institutions. Online banking systems that do not have proper KYC, customer due diligence, and transaction monitoring controls are vulnerable to being exploited by money launderers who can use various techniques, such as encryption, proxy servers, virtual currencies, prepaid cards, and online gambling, to conduct anonymous transactions123.
ACAMS CAMS Certification Study Guide, 6th Edition, Chapter 2, page 40-41, 43-44 ACAMS CAMS Certification Video Training Course, Module 2, Lesson 2.4, Money Laundering Using New Payment Methods
1, Fighting money laundering in the age of online banking, virtual currencies and internet gambling | ERA Forum
2, Financial crime risk management in digital payments | McKinsey
3, The Relationship Between Digital Banking and Financial Crime

According to the FATF Recommendation 10, financial institutions should conduct ongoing due diligence on the business relationship and scrutiny of transactions undertaken throughout the course of that relationship to ensure that the transactions being conducted are consistent with the institution's knowledge of the customer, their business and risk profile, including, where necessary, the source of funds. This is one of the core measures of customer due diligence (CDD) that aim to prevent and detect money laundering and terrorist financing risks.
= The main reference for this question is the document titled "International Standards on Combating Money Laundering and the Financing of Terrorism & Proliferation - The FATF Recommendations" published by the FATF in February 2018. You can access it by clicking here. You can also find more information about the CDD measures and the risk-based approach on the FATF website, the CFATF website, the Central Bank of Ireland website, and the Medium blog.