diff --git a/src/stan/callbacks/json_writer.hpp b/src/stan/callbacks/json_writer.hpp
index 5b6299c792..d791b8a737 100644
--- a/src/stan/callbacks/json_writer.hpp
+++ b/src/stan/callbacks/json_writer.hpp
@@ -146,7 +146,7 @@ class json_writer final : public structured_writer {
   /**
    * Writes the set of comma separated values in an Eigen (row) vector.
    *
-   * @param[in] v Values in a std::vector
+   * @param[in] v Values in an `Eigen::Vector`
    */
   template <typename Derived>
   void write_eigen_vector(const Eigen::DenseBase<Derived>& v) {
@@ -357,7 +357,7 @@ class json_writer final : public structured_writer {
    * @param key Name of the value pair
    * @param values vector to write.
    */
-  void write(const std::string& key, const std::vector<std::string>& v) {
+  void write(const std::string& key, const std::vector<std::string>& values) {
     if (output_ == nullptr) {
       return;
     }
@@ -365,14 +365,14 @@ class json_writer final : public structured_writer {
     write_key(key);
 
     *output_ << "[ ";
-    if (v.size() > 0) {
-      auto last = v.end();
+    if (values.size() > 0) {
+      auto last = values.end();
       --last;
-      for (auto it = v.begin(); it != last; ++it) {
+      for (auto it = values.begin(); it != last; ++it) {
         *output_ << process_string(*it) << ", ";
       }
     }
-    *output_ << v.back() << " ]";
+    *output_ << values.back() << " ]";
   }
 
   /**
@@ -380,7 +380,7 @@ class json_writer final : public structured_writer {
    * @param key Name of the value pair
    * @param values vector to write.
    */
-  void write(const std::string& key, const std::vector<double>& v) {
+  void write(const std::string& key, const std::vector<double>& values) {
     if (output_ == nullptr) {
       return;
     }
@@ -388,14 +388,14 @@ class json_writer final : public structured_writer {
     write_key(key);
 
     *output_ << "[ ";
-    if (v.size() > 0) {
-      auto last = v.end();
+    if (values.size() > 0) {
+      auto last = values.end();
       --last;
-      for (auto it = v.begin(); it != last; ++it) {
+      for (auto it = values.begin(); it != last; ++it) {
         write_value(*it);
         *output_ << ", ";
       }
-      write_value(v.back());
+      write_value(values.back());
     }
     *output_ << " ]";
   }
@@ -405,7 +405,7 @@ class json_writer final : public structured_writer {
    * @param key Name of the value pair
    * @param values vector to write.
    */
-  void write(const std::string& key, const std::vector<int>& v) {
+  void write(const std::string& key, const std::vector<int>& values) {
     if (output_ == nullptr) {
       return;
     }
@@ -413,14 +413,14 @@ class json_writer final : public structured_writer {
     write_key(key);
 
     *output_ << "[ ";
-    if (v.size() > 0) {
-      auto last = v.end();
+    if (values.size() > 0) {
+      auto last = values.end();
       --last;
-      for (auto it = v.begin(); it != last; ++it) {
+      for (auto it = values.begin(); it != last; ++it) {
         *output_ << *it << ", ";
       }
     }
-    *output_ << v.back() << " ]";
+    *output_ << values.back() << " ]";
   }
 
   /**
@@ -429,7 +429,7 @@ class json_writer final : public structured_writer {
    * @param values vector to write.
    */
   void write(const std::string& key,
-             const std::vector<std::complex<double>>& v) {
+             const std::vector<std::complex<double>>& values) {
     if (output_ == nullptr) {
       return;
     }
@@ -437,13 +437,13 @@ class json_writer final : public structured_writer {
     write_key(key);
 
     *output_ << "[ ";
-    if (v.size() > 0) {
-      size_t last = v.size() - 1;
+    if (values.size() > 0) {
+      size_t last = values.size() - 1;
       for (size_t i = 0; i < last; ++i) {
-        write_complex_value(v[i]);
+        write_complex_value(values[i]);
         *output_ << ", ";
       }
-      write_complex_value(v[last]);
+      write_complex_value(values[last]);
     }
     *output_ << " ]";
   }
diff --git a/src/stan/callbacks/structured_writer.hpp b/src/stan/callbacks/structured_writer.hpp
index fae1aed081..868c4c0cf3 100644
--- a/src/stan/callbacks/structured_writer.hpp
+++ b/src/stan/callbacks/structured_writer.hpp
@@ -106,8 +106,8 @@ class structured_writer {
    * @param key Name of the value pair
    * @param values vector to write.
    */
-  virtual void write(const std::string& key, const std::vector<double> values) {
-  }
+  virtual void write(const std::string& key,
+                     const std::vector<double>& values) {}
 
   /**
    * Write a key-value pair where the value is a vector of strings to be made a
@@ -124,14 +124,14 @@ class structured_writer {
    * @param values vector to write.
    */
   virtual void write(const std::string& key,
-                     const std::vector<std::complex<double>>& v) {}
+                     const std::vector<std::complex<double>>& values) {}
 
   /**
    * Write a key-value pair where the value is a vector to be made a list.
    * @param key Name of the value pair
    * @param values vector to write.
    */
-  virtual void write(const std::string& key, const std::vector<int>& v) {}
+  virtual void write(const std::string& key, const std::vector<int>& values) {}
 
   /**
    * Write a key-value pair where the value is an Eigen Matrix.
diff --git a/src/stan/model/model_base_crtp.hpp b/src/stan/model/model_base_crtp.hpp
index e0366a2f7a..5a64ced8c0 100644
--- a/src/stan/model/model_base_crtp.hpp
+++ b/src/stan/model/model_base_crtp.hpp
@@ -137,7 +137,7 @@ class model_base_crtp : public stan::model::model_base {
                    Eigen::VectorXd& vars, bool include_tparams = true,
                    bool include_gqs = true,
                    std::ostream* msgs = 0) const override {
-    return static_cast<const M*>(this)->template write_array(
+    return static_cast<const M*>(this)->write_array(
         rng, theta, vars, include_tparams, include_gqs, msgs);
   }
 
@@ -206,7 +206,7 @@ class model_base_crtp : public stan::model::model_base {
                    std::vector<int>& theta_i, std::vector<double>& vars,
                    bool include_tparams = true, bool include_gqs = true,
                    std::ostream* msgs = 0) const override {
-    return static_cast<const M*>(this)->template write_array(
+    return static_cast<const M*>(this)->write_array(
         rng, theta, theta_i, vars, include_tparams, include_gqs, msgs);
   }
 
diff --git a/src/stan/optimization/bfgs_linesearch.hpp b/src/stan/optimization/bfgs_linesearch.hpp
index 312459e378..e2c375a609 100644
--- a/src/stan/optimization/bfgs_linesearch.hpp
+++ b/src/stan/optimization/bfgs_linesearch.hpp
@@ -195,7 +195,8 @@ int WolfLSZoom(Scalar &alpha, XType &newX, Scalar &newF, XType &newDF,
  *
  * @param x1 Final point, equal to \f$ x_0 + \alpha p \f$.
  *
- * @param f1 Final point function value, equal to \f$ f(x_0 + \alpha p) \f$.
+ * @param func_val Final point function value, equal to \f$ f(x_0 + \alpha p)
+ *\f$.
  *
  * @param gradx1 Final point gradient, equal to \f$ g(x_0 + \alpha p) \f$.
  *
diff --git a/src/stan/services/sample/hmc_nuts_unit_e_adapt.hpp b/src/stan/services/sample/hmc_nuts_unit_e_adapt.hpp
index 332a720ca5..b6b345b8dd 100644
--- a/src/stan/services/sample/hmc_nuts_unit_e_adapt.hpp
+++ b/src/stan/services/sample/hmc_nuts_unit_e_adapt.hpp
@@ -103,7 +103,8 @@ int hmc_nuts_unit_e_adapt(
  * @param[in] init An std vector of init var contexts for initialization of each
  * chain.
  * @param[in] random_seed random seed for the random number generator
- * @param[in] chain chain id to advance the pseudo random number generator
+ * @param[in] init_chain_id chain id to advance the pseudo random number
+ * generator
  * @param[in] init_radius radius to initialize
  * @param[in] num_warmup Number of warmup samples
  * @param[in] num_samples Number of samples