No there are no disadvantages of using SSL certificate. However, using SSL certificate doesn't sounds that you ignore other essential factors of website security. Sometimes web developers write poor code, which is an opportunity for hackers to search back doors in your website.
According to my knowledge, most of the attacks on website happens due to vulnerable coding, so make sure you recheck your website scripts. In addition, avoid the use of unnecessary free plug-ins and modules on your site.
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"I'm not anti-social; I'm just not user friendly"
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