Can there be a danger of safety?
This is a frequent form of the verb 存在 which is used transitively (i.e. it accepts an accusative phrase).

You can break down the sentence as follows: 


很多候选药物 -> (subject) many candidate drugs
都 -> (adverb) all
存在 -> (transitive verb) present
严重的 -> (noun modifier with 的, lax modification) serious
安全 -> (noun modifier without 的 = close modification) safety
隐患 -> (noun, object) hidden dangers, risks

It is worth noting the difference between 严重的 and 安全. Grammatically they have the same purpose, i.e. modifying the noun, but the first is a pure adjective 严重 and is therefore "applied" to the noun by interposing a 的. The second 安全 has a double value both as noun, as in 安全第一 (safety first), or as adjective, as in 这个区域很安全 (this area is [very] safe). Here 安全 is used as an adjective. It doesn't require 的 because: 
安全 is inherently a noun, and
的 would be used to determine the strength of the specification. 安全的 poses more emphasis on 安全 (risks [of/for] the safety); no 的 poses more emphasis on the modified noun, thus forming a phrase with 隐患.

Finally you can translate the sentence as:
All candidate drugs present serious safety risks.