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Templates {{1}}, {{2}}, {{3}} etc warn readers/editors that a typo exists in the page they are reading/editing. If {{{{{1}}}}} is called, you probably meant the parameter {{{1}}} (as {{{{{{1}}}}}} with triple braces), but in fact only double braces were used, invoking {{{{{1}}}}}. In addition to a warning, it also adds pages to Category:Templates with incorrect parameter syntax.
However, the most problems have been caused by omitting the first brace "{" of a parameter and getting {{{{{1}}}}}}, as invoking Template:{{{1}}} +"}" rather than parameter {{{1}}}. This can be an insidious problem, especially when the transclusion of Template:{{{1}}} is hidden, so that the effect is invisible to the person editing a page. For that reason, Template:{{{1}}} now issues a warning to the user.
With that warning, the prior invisible access to Template:{{{1}}} can now be understood to be a formerly unseen problem coded within a page.
Note: this will also pick up several variations such as {{{{{1}}}|}} for {{{{{{1}}}
