diff --git a/src/lib/broadcast.jl b/src/lib/broadcast.jl
index 6dbfdb829..3a322c5fe 100644
--- a/src/lib/broadcast.jl
+++ b/src/lib/broadcast.jl
@@ -170,14 +170,13 @@ _broadcast(f::F, x...) where F = materialize(broadcasted(f, x...))
 collapse_nothings(xs::AbstractArray{Nothing}) = nothing
 collapse_nothings(xs) = xs
 
-_dual_purefun(::Type{F}) where {F<:Function} = Base.issingletontype(F)
-_dual_purefun(::Type) = false
+_dual_purefun(::Type{F}) where {F} = Base.issingletontype(F)
 _dual_purefun(::Type{typeof(^)}) = false  # avoid DomainError from negative powers
 
 _dual_safearg(x::Numeric{<:Real}) = true
 _dual_safearg(x::Ref{<:Numeric{<:Real}}) = true
-_dual_safearg(x::Union{Type,Val,Symbol}) = true  # non-differentiable types
-_dual_safearg(x) = false
+_dual_safearg(x::Union{Val, Symbol, Char, AbstractString}) = true  # non-differentiable types
+_dual_safearg(x::T) where {T} = Base.issingletontype(T) || Base.issingletontype(eltype(T))
 
 @adjoint function broadcasted(::AbstractArrayStyle, f::F, args...) where {F}
   T = Broadcast.combine_eltypes(f, args)
@@ -226,9 +225,9 @@ end
 import ForwardDiff
 using ForwardDiff: Dual
 
-dual(x, p) = x
 dual(x::Real, p) = Dual(x, p)
-dual(x::Bool, p) = x
+dual(x::Bool, p) = x  # must ignore
+dual(x, p) = x  # safe to ignore: trust _dual_safearg() elsewhere
 
 function dual_function(f::F) where F
   function (args::Vararg{Any,N}) where N
@@ -239,7 +238,14 @@ function dual_function(f::F) where F
   end
 end
 
-@inline function broadcast_forward(f, args::Vararg{Any,N}) where N
+@inline function broadcast_forward(f::F, args::Vararg{Any,N}) where {F,N}
+  Base.issingletontype(F) || @warn ("""Zygote's dual number broadcasting (as used on GPU arrays) cannot track gradients with respect to `f`,
+      and `f` appears to be a closure, or a struct with fields (according to `issingletontype(typeof(f))`).
+      typeof(f) = $(F)""") maxlog=1 _id=hash(F)
+  for a in args
+      _dual_safearg(a) || error("""Zygote's dual number broadcasting (as used on GPU arrays) cannot handle this argument.
+      typeof(a) = $(typeof(a))""")
+  end
   valN = Val(N)
   out = dual_function(f).(args...)
   eltype(out) <: Dual || return (out, _ -> nothing)
diff --git a/test/cuda.jl b/test/cuda.jl
index 5cb1c8cdc..ea2cbeb82 100644
--- a/test/cuda.jl
+++ b/test/cuda.jl
@@ -48,6 +48,19 @@ end
   @test gradient(x -> sum(exp.(x)), Diagonal(a_gpu))[1] isa Diagonal
   # non-differentiables
   @test gradient((x,y) -> sum(x.^2 .+ y'), a_gpu, a_gpu .> 0)[2] === nothing
+  
+  # Errors -- #1215
+  y = complex.([4,1]) |> cu
+  x = complex.([3,2]) |> cu
+  function f1215(x, y) 
+      x = 2 .* x
+      return sum(abs2.(x .- y))
+  end 
+  @test_throws ErrorException gradient(()-> f1215(x,y), Zygote.Params([x]))
+  
+  # From #1018
+  @test gradient((x,y) -> sum((z->z^2+y[1]).(x)), [1,2,3], [4,5]) == ([2, 4, 6], [3, 0])
+  @test_skip gradient((x,y) -> sum((z->z^2+y[1]).(x)), cu([1,2,3]), cu([4,5]))  # if not right, should ideally be an error
 end
 
 @testset "sum(f, x)" begin