diff --git a/pandas/_libs/reduction.pyx b/pandas/_libs/reduction.pyx
index c892c1cf1b8a3..bf940eb03e06f 100644
--- a/pandas/_libs/reduction.pyx
+++ b/pandas/_libs/reduction.pyx
@@ -528,7 +528,8 @@ def apply_frame_axis0(object frame, object f, object names,
 
             try:
                 piece = f(chunk)
-            except:
+            except Exception:
+                # We can't be more specific without knowing something about `f`
                 raise InvalidApply('Let this error raise above us')
 
             # Need to infer if low level index slider will cause segfaults
@@ -539,6 +540,7 @@ def apply_frame_axis0(object frame, object f, object names,
                 else:
                     mutated = True
             except AttributeError:
+                # `piece` might not have an index, could be e.g. an int
                 pass
 
             results.append(piece)
diff --git a/pandas/_libs/tslibs/c_timestamp.pyx b/pandas/_libs/tslibs/c_timestamp.pyx
index a45b8c9b35dfa..dfa66d7e2d862 100644
--- a/pandas/_libs/tslibs/c_timestamp.pyx
+++ b/pandas/_libs/tslibs/c_timestamp.pyx
@@ -140,7 +140,8 @@ cdef class _Timestamp(datetime):
 
         try:
             stamp += zone.strftime(' %%Z')
-        except:
+        except AttributeError:
+            # e.g. tzlocal has no `strftime`
             pass
 
         tz = ", tz='{0}'".format(zone) if zone is not None else ""
diff --git a/pandas/_libs/tslibs/timedeltas.pyx b/pandas/_libs/tslibs/timedeltas.pyx
index d24aafae0967d..ad7c32ca31940 100644
--- a/pandas/_libs/tslibs/timedeltas.pyx
+++ b/pandas/_libs/tslibs/timedeltas.pyx
@@ -228,8 +228,13 @@ def array_to_timedelta64(object[:] values, unit='ns', errors='raise'):
     # this is where all of the error handling will take place.
     try:
         for i in range(n):
-            result[i] = parse_timedelta_string(values[i])
-    except:
+            if values[i] is NaT:
+                # we allow this check in the fast-path because NaT is a C-object
+                #  so this is an inexpensive check
+                iresult[i] = NPY_NAT
+            else:
+                result[i] = parse_timedelta_string(values[i])
+    except (TypeError, ValueError):
         unit = parse_timedelta_unit(unit)
         for i in range(n):
             try:
@@ -309,7 +314,7 @@ cdef inline int64_t cast_from_unit(object ts, object unit) except? -1:
     return <int64_t>(base * m) + <int64_t>(frac * m)
 
 
-cdef inline parse_timedelta_string(object ts):
+cdef inline int64_t parse_timedelta_string(str ts) except? -1:
     """
     Parse a regular format timedelta string. Return an int64_t (in ns)
     or raise a ValueError on an invalid parse.