Can there be a danger of safety? I presume this is good Chinese, but I would appreciate your opinions, because it confuses me.

由于肥胖的形成原因很复杂，因此减肥药的研制困难重重，很多候选药物都存在严重的安全隐患。

It seems to say:


很多候选药物存在 many candidate drugs exist


but 存在 must mean 有 here. 有严重的。。。。 Is 存在 often used this way?


安全隐患 seems to say 'safe hidden dangers' which is somewhat paradoxical, 'safe dangers'. They might mean 'safety dangers, dangers to safety' but was there ever a 'safe danger'? The one excludes the other. They must of course mean potentially dangerous side effects.


I'm pretty sure I understand the sentence correctly, but is it good Chinese?
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.